שמע ישראל ה' אלו-הינו ה' אחד, "Hear O Israel the Lord our God the Lord is One.⁠"According to the plain meaning of the text the reason that Moses mentioned three names of God, i.e. Hashem elokeynu Hashem, needs explaining. Had he only mentioned ה' אחד, there would have been a chance for the nations to understand the name Hashem as the way the Jews describe the god of the Gentiles in their language. This is why Moses had to add the word אלו-הינו, to make plain that Hashem is the name of our God, the God of the Jewish people. Conversely, if Moses had merely said ה' אלו-הינו אחד, the nations might have said that while it is true that there is only a single national Jewish God, their own national god was also unique in his own right. Therefore Moses had to phrase this declaration of faith and acceptance in such a way that it unmistakably reflected our belief that 1) there is only one God deserving this name, 2) that He is the God of the Jewish people, 3) that He is unique in the universe, there is no other God deserving the title. He has no partners, is not an amalgamation of different powers working in tandem. His uniqueness is unmatched on earth, below it, or in the celestial regions. In the future He will be recognized as such universally as promised by our prophets, especially Zecharyah 14,9: "it will be on that day that the Lord will be One and His name will be One.⁠"
If Moses here said אלו-הינו, whereas so far throughout the Book of Deuteronomy he had almost invariably spoken of אלו-היך when addressing the Jewish people, this was because he wanted to include himself in the Jewish community who accepted the Oneness of the Lord.

An interesting comment by Rabbi Eliezer from Germeize, (the author of the Rokeach, a pupil of Rabbi Yehudah Hachassid): he claims that the first time Moses mentioned Hashem he referred to God who preceded the universe, the word אלו-הינו refers to God as He is perceived while the present universe is in existence; the third time Moses refers to Hashem he refers to the time when this universe as we know it will no longer exist. While there are people who relate to Him, He is perceived as אלו-הינו, whereas when there are no creatures to thus acknowledge Him He is simply known as Hashem.

You should realize that the whole subject of God's uniqueness relates to serving God with one's heart. The Torah refers to this in 11,13 where we read the instructions "to serve him with all your heart.⁠" Seeing that people who speak to another sometimes mean what they say, i.e. concentrate on what they are saying and sometimes they don't, being distracted, the Torah writes "שמע,⁠" which includes the mind and the ear being attuned to each other. One is not only to relate to God by hearing with one's ear but by opening one's heart to what one is about to hear with one's ear. Whenever the subject of God's Unity comes up it is an absolute requirement that it not be treated offhandedly, lightheartedly, without adequate concentration of one's mind. When saying the above words one must not only make sure that one's own ears hear them but one must be certain that one's heart is attuned at the same time.
Seeing that when one hears a person recite the שמע that person cannot be certain if at that moment the mind of the one reciting it is on the same wavelength as his mouth, or if his mind is on other matters altogether, the letter ע in this word is written in larger script as is the letter ד, at the end of the verse. When read together these two letters spell the word עד; in other words, we are warned that there is a witness, i.e. the Lord Himself, Who is aware if we have concentrated on what we are saying when reciting this commitment or if we have only been going through the motions. From all the above it is clear that a person must be very careful when reciting the קריאת שמע not to undo the good he plans to do thereby by performing the commandment in an offhanded manner. We were taught in Berachot 34 that one teaches a reader (in the Synagogue) to concentrate on what he is saying even if one has to physically strike him to drive home the lesson.

You should know that Gan Eden (after death) was not created except to reward the people who acknowledge God's Unity not only as a platitude but by concentrating on what they are saying. Admitting God's Uniqueness is the other side of the coin of denying the validity of any form of idolatry. On the other hand, anyone who acknowledges any form of idolatry automatically denies the Oneness and Uniqueness of the Lord. The principal reason that purgatory, gehinom, and its seven kinds of fires have been created was to repay the people guilty of idolatry. This is why you find the word גן thirteen times in Parshat Bereshit (compare Genesis 2,8; 9; 10; 15; 16; 3,1; 2; 3; 8;9-10; 23;24;) By way of contrast you find the word אש, fire, thirteen times in our Parshah here. This is to teach you that everyone who has had the right thoughts when saying the word אחד=13 in the line שמע ישראל ה' אלו-הינו ה' אחד will be saved from the fires of Gehinom, seeing that he will merit the thirteen levels of elevations available in Gan Eden.
We are told in Ketuvot 77 that Rabbi Joshua ben Levi once met Rabbi Shimon ben Yochai (in a dream) when the latter was seated on thirteen golden mattresses. This is an allusion to the thirteenth and highest level in Gan Eden.

A Midrashic approach: The reason that the verse שמע ישראל is written here after the Ten Commandments is to teach the people that when God used the attribute אנכי when introducing Himself at the beginning of the Ten Commandments, He referred to this אחדות of His, His uniqueness. Rabbi Nathan used the Ten Commandments (the text) to counter the claim of the heretics who believe that there are two separate and independent domains of authority in the universe. When the Lord stood at Mount Sinai and began the decalogue with the words "I am the Lord your God who has taken you out of Egypt,⁠" this was equivalent to a challenge. Who dared oppose God at that time? Seeing that this verse שמע ישראל introduces our declaration of God's Uniqueness, Moses saw fit to commence numerous verses in the Book of Deuteronomy with the words שמע ישראל. Some samples of such verses are found in Deut. 9,1; 20,3; 27,9. There are many others.
We read in the Midrash (Devarim Rabbah Lieberman edition page 66) that the words שמע ישראל recall the time when Yaakov was worried that may be one of his sons was not whole-hearted in his loyalty to Hashem and he called in his sons and confronted them on the issue by saying ושמעו אל ישראל אביכם, (Genesis 49,2). What he meant was: "listen to the One whom your father Israel serves, i.e. to God.⁠" Upon hearing this, the sons replied in unison שמע ישראל ה' אלו-הינו ה' אחד. Ever since the Jewish people have adopted the declaration made by the 12 sons of Yaakov as one of abiding faith in God also their own declaration of faith, pronounced every day. The formula has been amended to read: "שמע ישראל אשר במערת המכפלה ה' אלו-הינו ה' אחד "hear O Israel who is buried in the cave of Machpelah the Lord our God, the Lord is One.⁠" (Compare Devarim Rabbah Lieberman edition page 67).
Our sages also commented in Devarim Rabbah (Lieberman edition page 77) that when the people had stood at Mount Sinai they had vowed נעשה ונשמע, "we will do and we will listen.⁠" Once they had made the golden calf Moses said to them that seeing they had already reneged on the first half of their undertaking they should at least honor the second part, i.e. the נשמע, by reaffirming their faith in the one and only God by saying the שמע ישראל on a daily basis. This matter can best be illustrated by a parable. A king betrothed a wife by giving her two 2 pearls. When she lost one he said to her: "safeguard the remaining one.⁠" Thus far Midrash Rabbah.

A more rational approach to our line: we all know of many phenomena both above terrestrial earth and below in our world which exercise their influence on our lives in one form or another. It stands to reason that above all of these phenomena there is a hand which directs them all. The proliferation of the phenomena we witness must have its origin in a single force (compare Shaar Hayichud Chovot Halevavot chapter 5). Just like the number 1 is the first in a string of numbers, so Unity is the first (in terms of time) of a number of phenomena. Seeing that we are all witnesses to so many and different phenomena in the universe, it is quite clear that all of them must be derivatives of an original phenomenon, the Ultimate Cause. Even though the name "one" is applied to many things this description is misleading and inaccurate. It is a habit of people to use terms which, strictly speaking, apply to only one phenomenon and to describe other phenomena as possessing such characteristics. For instance, even in the Torah we find the Tabernacle referred to as אחד, "one,⁠" (Exodus 26,6) although we all know that it was composed of many different parts. The reason the Torah described it on that occasion as "one,⁠" was that all its constituent parts had been joined together and placed in their correct positions so that the finished product appeared to be "one.⁠" Nonetheless the Tabernacle was subject to being dismantled and to no longer appear as a single unit.
We find that God told the prophet (Ezekiel 37,16) "take for yourself 'one' tree (or piece of wood).⁠" The expression אחד in that verse is a misnomer as there is only one phenomenon to which that definition can truly be applied, but the prophet describes it as such as he wants to portray a concept, i.e. the symbol of unity, something undivided. Although man is composed of 248 limbs the composite of these 248 limbs is called "one man.⁠" Even the raw material man is made of is a composite of 4 elements; nonetheless we speak of "flesh" as if it consisted of a single raw material. All of the components of man will disintegrate at death proving that what was considered as "one" during his lifetime was in reality nothing of the kind. [Science may be defined as the search for the original single cause of the universe. Ed.]. Even amongst the celestial beings, the angels which are made of a uniform raw material and are therefore not subject to disintegration the term אחד cannot be applied in the true meaning of the word, seeing that each angel is only one of many such angels, so where is his uniqueness? The same applies to our souls. Although it is not an amalgam of elements such as our body, there are thousands of souls so how could a soul be truthfully described as אחד, truly unique? In other words, none of the phenomena in the universe can accurately be described as אחד with the exception of the Lord God Who is truly one of a kind in the absolute sense of the word. This is what the prophet Isaiah 40,25 meant when he said, paraphrasing God: ואל מי תדמיוני ואשוה, "to whom do you wish to compare Me, to whom can I be likened?⁠"

A kabbalistic approach: the words שמע ישראל may be understood as "bend your ear and listen.⁠" This verse comprises the subject of true uniqueness which is accepted by all the students of Kabbalah as the mystical dimension of the ten emanations. It is man's task to unify these ten emanations and to ensure they are joined together not only in a descending but also in an ascending direction [It is a common perception that the concept of the emanations is intended to facilitate our understanding of how something totally abstract, disembodied, can be transformed into a physical, substantive universe. Kabbalists understand it as the task of man to transcend the physical universe they find themselves in and to strive for a union with the source, Hashem, by means of these emanations. Ed.]. The word שמע is perceived as an instruction to create such a bond, union. The word occurs in this context in Samuel I 15,4 וישמע שאול, where it could not mean that Saul had heard with his ears. It means that Saul mustered the troops, i.e. made them join together. Psalms 18,45 is another example of the word שמע meaning something beyond merely hearing with a physical organ of the body. It speaks about the assimilation of such "hearing,⁠" i.e. obedience, as a natural result of "digesting" what one's ear has heard.
The word Hashem is also to be understood as similar to לך ה', "it is yours O Hashem" (Chronicles I 29,11). That verse combines the three highest spiritual attributes (emanations) אלו-הינו, הגדולה, הגבורה. The second time the word Hashem occurs in our verse is a reference to the emanation תפארת and the emanations below that until the lowest emanation, "the completion of the structure.⁠"
The word אחד at the end of our verse comprises all the emanations. The letter א in that word refers to the One whom our mental capacities cannot define. The letter ח refers to all the eight emanations which accompany Him; The letter ד refers to the tenth emanation, the crowning glory known as עטרת זהב גדולה, and the word אחד, is not to be separated from the rest of the verse. [I suppose the author stresses this as by definition that which is אחד, one, unique, is distinct and separate from anything else already. Ed.]. Here the Torah tells us that all the ten emanations are to be joined as if they were not multiples but one. The reason it is appropriate for this process of joining the emanations together to proceed from the bottom up, is because we have a principle that in matters of sanctity we always proceed from a lower level to a higher level, never the reverse.
Concerning the letter ד in the word אחד i.e. the lowest emanation known as מלכות, Isaiah 63,12 says בוקע מים מפניהם לעשות לו שם עולם, "Who divided the waters before them to make Himself a name for all time.⁠" We refer to this manifestation of God as the lowest of the emanations in our prayers every day when we recite מלכותך ה' אלו-הינו ראו בניך בוקע ים לפני משה זה אלי ענו, "Your manifestation Lord our God as the emanation מלכות Your children have witnessed when You split the sea before Moses and they answered: "this is My God.⁠" [The version of this prayer quoted here is similar to that in Machzar Vitri].
Seeing that the verse שמע ישראל does not contain an explicit reference to the emanation מלכות, our sages have seen fit to append the line ברוך שם כבוד מלכותו לעולם ועד, "may the name of His glorious emanation מלכות be blessed forever more.⁠" Even though Moses did not mention this attribute explicitly we do find it alluded to in the letter ד at the end of the verse. Our sages (Pesachim 56) illustrated the problems our sages encountered in adding something Moses had not seen fit to add but which our patriarch Yaakov reportedly added, by means of a parable. The daughter of a king who entered the kitchen smelled a delicious dish which had wonderful condiments added to it. She was very eager to eat some of it immediately. She said to herself that if she were to ask for this outright now it would be considered ill-mannered. On the other hand, if she were to wait until evening when the dish would be served she would experience physical pain during the time she had to wait. When her attendants became aware of this they brought her some of the condiment surreptitiously. As a result, the mind of the princess was put at rest. The parable symbolizes the Israelites (princess) who had become aware of the blissful effect of the emanation מלכות. Her attendants, i.e. the Shechinah, realized the Israelites' strong desire to exalt God by making reference to this emanation. If they would not be allowed to do so they might pine away from distress. Giving the princess some of the condiment secretly is equivalent to the sages allowing the Jewish people to recite the line ברוך שם sotto voce, in an undertone, so as not to reflect on the spiritual presumptuousness of the Jewish people. In kabbalistic terms the compromise thought up by the Shechinah, and later our sages, means that reciting this line in an undertone is equivalent to reciting God's "lower level" of unity and praising it. This is also why the line ברוך שם comprises 6 words just as the verse שמע ישראל comprises 6 words, each alluding to the six extremities of the terrestrial universe, i.e. the four directions of the compass plus "up" and "down.⁠" Adding the letter ד from אחד completes the number 10 so that all the ten emanations are represented. The 6 words in the line שמע ישראל allude to the celestial regions, whereas the six words in the line ברוך שם allude to the terrestrial regions of the universe in each of which the Lord is supreme, unique, unmatched.
The Sefer Habahir (item 27) contains the following comment: The students asked their rabbi about the meaning of the letter ד in the word אחד at the end of our verse. He told them by means of a parable that they should perceive of ten kings, all wealthy, all congregating in a single place. One of the ten, while wealthy, was not as wealthy as the others. Due to this relative poverty he was considered as דל, "poor.⁠" Thus far the text in the Sefer Habahir. The ten kings are the ten emanations all of which congregate in the celestial spheres, except the lowest emanation מלכות which is part of the עולם העשיה, the terrestrial universe, (at least perceptually. Ed.). When people in the terrestrial universe declare the Unity of Hashem they must therefore concentrate on all the ten emanations or they would not do justice to their task. The word אחד therefore has especial significance. The number 10 represents the Power of the One who "invented" the ten emanations
Compare the smallest unit in our terrestrial universe the "point.⁠" A point is not really only a point, as no matter how small it is it has width, length, and depth. Not only that, but the area (or imaginary line) called length has a beginning, a middle and an end. The same is true for the area called width and that called depth. This already makes a "point" something consisting of no less than nine definable areas. Add to this the space in the universe this "point" occupies and we are talking about 10 units of space. This demonstrates the importance of the number 10 as an indispensable number; in terrestrial terms you may call it an irreducible minimum. When we translate this into the aleph bet, the smallest letter the י, though perceived and spoken of as no more than a "point,⁠" נקודה, actually represents both the number 1 and the number 10. A similar principle applies to the letter ה of the tetragrammaton, the Holy name of Hashem. Being three-sided it has three times beginnings, middles and ends in each line. Add the space it occupies and you find it also represents the number 10. Or, you simply view the letter ה as a combination of the letter י, i.e. the left, lower part, plus the letter ו. In either event you wind up with the number 10 (at least).
When we recite the Kaddish, this also has to include concentrating on the ten emanations. The words אמן יהא שמיה רבה מברך are perceived as being said on the קו האמצעי, the center line of the diagram of the ten emanations. Five of the emanations are above this "center line,⁠" whereas the other 5 are below making a total of 10. (The author proceeds to demonstrate similar patterns in the kedushah claiming that the sages of the Great Assembly who formulated that prayer deliberately chose to commence with the word כתר to allude to the highest, the tenth of the emanations. He continues in this vein to analyze the visions described by Ezekiel and quoted in the קדושה דסדרא in the daily ובא לציון גואל prayer).

According to the Midrash Devarim Rabbah near the end of Parshat Vaetchanan, the reason that the line ברוך שם is recited sotto voce is that it is the formula used by the angels to praise the Lord, and we do not want to provoke the angels by copying them. According to that Midrash, Moses learned this secret formula while overhearing the angels when he was on Mount Sinai. When Moses taught the Torah to Israel he told them that everything he taught them he had learned himself from the Torah (God) with the exception of the line ברוך שם which he had learned from the ministering angels. He advised the Israelites to recite this line silently. Only on the Day of Atonement, when, thanks to our sins having been forgiven we are on a spiritual par with the angels, do we recite this line without fear of arousing their jealousy. The fact that on that day we neither eat nor drink, just like the angels, coupled with the fact that we don white garments, makes us sufficiently like the angels to praise God in the way they do.