ברית תורה שבעל פה
כתב לך את הדברים האלה כי על פי הדברים האלה כרתי אתך ברית ואת ישראל
Write these words for yourself, for according to these words have I sealed a covenant with you and Israel.
The Holy One did not enter a covenant with the Jewish people but for the Oral Torah as it says “for according to these words have I sealed a covenant with you and Israel.” 
What exactly is this covenant, and why was it sealed specifically through the Oral Torah? The essence of this covenant is the resting the Shechina, the Divine Presence, among Bnei Yisrael. To understand what this covenant signifies we must examine first what the resting of the Shechina means, and what is so significant about this Divine revelation.
The Zohar states,
from the day that the Beis HaMikdash was destroyed and the sacrifices were annulled, all that remains for G-d are the words of the Torah and Chidushei Torah of the mouth.
These words of the Zohar are astounding. From the Gemara we learn that “since the day that the Temple was destroyed, the Holy One, Blessed is He, has nothing in His world but the four cubits of Halacha” , teachings which have been passed down from generation to generation. Yet the Zohar illuminates for us that the novelty of the Torah, the innovation and newness found in it by those who learn it, is what sustains G-d’s Divine presence in the world. They are the reason G-d finds pleasure in His world. This warrants further explanation. Let us begin by explaining the words of our Sages concerning the building of the Mikdash and its destruction, and through this we will be able to understand the necessary prerequisites to G-d’s Shechina dwelling among Bnei Yisrael. The Gemara states
Rav Yehudah said in the name of Rav: what is the meaning of that which is written:”Who is the wise man who will understand this, etc.”? This matter [i.e. why the land was lost] was asked of the Sages and of the prophets, yet they could not explain it, until the Holy One, Blessed is He, Himself explained it, for it is written:”and Hashem said: Because of their forsaking my Torah etc.” … that they did not recite the blessing on the Torah first.
The Ran quotes Rabbeinu Yonah who explains how Rav knew that the land was destroyed due to their lack of reciting the blessing on the Torah first
If the reason [the land was destroyed] was because they weren’t learning at all (as is implied from the passuk), why weren’t the sages and prophets able to explain this? It’s a simple, known reason. Rather, certainly they were busy with Torah study—and therefore the sages and prophets were stumped as to why the land was destroyed. Only G-d Himself was able to explain this, for he knows the depths of people’s souls and he knew that they were not making the blessings on Torah study, meaning that it was not so important in their eyes to warrant a blessing on its study, because they were not studying it for the sake of heaven.
But the question still stands: is it possible that the Sages of Am Yisrael and the prophets, who were experts in all the internal workings of the Jewish nation’s soul and its secrets did not realize that Bnei Yisrael no longer valued the Torah and no longer studied it for the sake of heaven? The question is magnified by the ב"ח’s version of the Gemara which adds that the question was posed to the ministering angels as well. How could it be that angels who know all the thoughts in people’s hearts did not notice that Bnei Yisrael weren’t occupied with Torah for its own sake? Leaving these questions aside, it’s even more difficult to explain why the Beis HaMikdash was destroyed because of their lack of Torah study for its own sake, when our Sages clearly teach us that Torah study even not for its own sake is still a great mitzvah and a person should learn even though it is not for its own sake, for through learning it not for its own sake, he will eventually come to learn it for its own sake? Furthermore, during the time of the destruction, Bnei Yisrael were guilty of far greater sins—adultery, idol worship, and murder, and the Gemara elsewhere states that it is because of these three sins that the Beis HaMikdash was destroyed. So how can we reconcile these discrepancies?
Perhaps we can reconcile this discrepancy with the words of the Medrash relating the mitzvah of building a Temple. Clearly the reason for its destruction is rooted in the rationale behind its being built—i.e., when the reason for which it was built is no longer present, it is inevitable that it will be destroyed. The Medrash states,
Is there such a thing as merchandise whose seller is sold with it? Said Hashem [to the Jewish people]: I have sold you My Torah, and I have been sold with it, as it states “let them take for Me a portion.” This is likened to a king who had an only daughter. Came one of the kings, took the daughter and wanted to go back to his own land to marry her. Said the king to him: “my daughter is an only child. To part with her—that I cannot bear. To tell you not to go—that I cannot do, for she is your wife. So do this one favor for me: every place you go, make a small chamber for me so I can live with you, for I cannot leave my daughter.” So said the Holy One, Blessed is He, to Bnei Yisrael: I gave you the Torah. I cannot bear to part with it and I cannot tell you not to take it. Rather, in every place you go, make one house for me so that I may dwell in it, as the passuk states: “and they shall make for Me a sanctuary.”
The Medrash opens the door for us to understand the concept of Divine Presence among Bnei Yisrael. G-d said “to part with her [the Torah]- that I cannot bear.” Any place where His Torah is studied, there He dwells. This is the reason He commanded them and they shall make for Me a sanctuary- because G-d cannot bear to part with the Torah He gave them. This is the meaning of the continuation of the passuk so that I may dwell among them.
This also sheds light on the words of R’ Chalafta ben Dosa of Kfar Chanania
How do we know this even of one (who sits and engages in Torah study- that the Divine Presence rests with him)? For it is said:”In every place where I cause My Name to be mentioned, I will come to you and bless you.”
Every place where Torah is studied as it should be, even by one person, G-d says “ to part with her- that I cannot bear.”
Come and see what the Zohar states,
How beloved is the Torah before G-d, for in every place where the Torah is heard the Holy One, Blessed is He, and all His entourage listen to every word, and the Holy One, Blessed is He, comes to dwell with him, as it says;”In every place etc.” 
But at first glance this parable to a king and his daughter doesn’t fit what it’s meant to represent. When a person marries off a daughter, it is understood that she leaves her father’s household to go to her husband’s. No person can be in two places at once. So too with any gift that is given by one person to another—it is transferred from the giver’s domain to the recipient’s. So we can understand what the king said—“my daughter is an only child, to part with her—that I cannot bear.”But someone who confers wisdom on another, his own knowledge is in no way diminished. The teacher does not have to part with that which he is teaching; they can both retain and gain from that knowledge. Why, then, did G-d tell Bnei Yisrael “I cannot bear to part with it [the Torah],” and command them to make a dwelling place for Him?
In truth, when G-d gave the Torah to Am Yisrael, it wasn’t merely knowledge and wisdom which he imparted to them; rather he gave them the power to ”control” the Torah, and to use the Torah to dominate the whole creation. From the moment the Torah was given, one does not even rely on a Bas Kol, a Heavenly echo, to decide in Halacha because לא בשמים היא שכבר ניתנה תורה מהר סיני, it [the Torah] is not in heaven, for the Torah was already given [to man] at Har Sinai. The Gemara relates how R’ Eliezer and R’ Yehoshua had a disagreement concerning the status of the oven of the coiled serpent. R’ Eliezer’s opinion was rejected even though he shook the foundations of the world—a tree uprooted itself, the water canal flowed backward, the walls of the Beis Medrash leaned and were about to fall, and even a Bas Kol proclaimed he was right, saying “what argument do you have with R’ Eliezer whom the Halacha follws in all places!.” Nevertheless, these things were inadmissible as evidence of R’ Eliezer’s correctness; his opinion was not accepted. When R’ Yehoshua stood up and stated לא בשמים היא, [Torah] is not in Heaven, he set a halachic principle applicable not only in that case but for all future times, namely, that G-d gave the Torah to Am Yisrael and gave its scholars the authority to set Halacha.
Furthermore, we find in the Gemara,
At that moment, they were disputing the following Mishna in the Heavenly Academy: If the Bahares (i.e.a snow-white spot, one of the skin discolorations symptomatic of tzaraas) preceded the white hair, [the Baheres] is tamei. But if the white hair preceded the Baheres, it is tahor. If there exists a doubt as to which came first, the Holy One, Blessed is He, says the leprous mark is tahor, and the entire Heavenly Academy say it is tamei. As a result of this dispute they said, “who will decide this issue? Rabbah bar Nachmani will decide.” They chose him to decide the issue, for Rabbah bar Nachmani had once said, “I am unique in my knowledge of Negaim; I am unique in my knowledge of Oholos.” They sent an agent after him to fetch him. However, the Angel of Death could not approach him since his mouth did not cease from its recitation of Torah. At that point a wind blew, and made loud noises among the reeds. [Rabbah bar Nachmani] thought it was a brigade of horse-men who were coming to arrest him. He said, “may the soul of that person (myself) pass on so that he will not be given into the hands of the government.” As he was dying, he said, “Tahor, tahor.” A heavenly echo issued forth and said, “fortunate are you, Rabbah bar Nachmani, for your body is tahor and your soul departed with the utterance of the word tahor!”
G-d and the Heavenly Academy argued as to whether a doubt in tumas negaim is tamei or tahor. Rabbah bar Nachmani who had the credentials to decide this matter ruled tahor in accordance with Hashem. Despite this, the Rambam rules tamei. The Kesef Mishna explains the Rambam’s reason:
Since he [Rabbah bar Nachmani] said this at the time of the departing of his soul, this is included in the ruling that “[Torah] is not in heaven”, and should therefore not be relied upon against the common ruling that we rule like Tana Kamma (who ruled tamei).
See how far reaching is the power of the Torah, that G-d in his mercy vested in Am Yisrael the ability to overpower, so to speak, G-d’s own opinion.
Not only did G-d give Am Yisrael the authority over the Torah, He also gave them the power to manipulate nature via the Torah. As is brought in the Yerushalmi
The features of virginity of a three year old girl who cohabited do not heal. But if the Beis Din vote to make the year a leap year (thereby causing her third birthday to have not yet arrived) her features of virginity will heal. This is what the passuk “to the G-d who fulfills for me” is referring to.
G-d gave His world over to those who learn Torah and toil in it in purity, to build and to destroy, to uproot and to plant.
This is a wondrous power which Bnei Yisrael have—to use their G-d-given brain to augment and expound on the Torah. Bnei Yisrael control its halacha through their knowledge. This is why G-d said to them “I gave you the Torah, but I cannot bear to part with it…in every place you go, make one house for me so that I may dwell in it.” This is what G-d bequeathed to the Jews—this ability to handle the Torah, interpret it and enhance it. Perhaps now we can explain the words of our Sages G-d did not enter a covenant with the Jewish people but for the Oral Torah, as the passuk states, “… for according to these words have I sealed a covenant with you and Israel.” What is unique about the Oral Torah more than the Scripture? Why is the covenant premised on the Oral Torah specifically? Based on what we’ve learned above, it is clear. The covenant with the Jewish people and G-d resting His Shechina among the Jews is dependent on the Oral Torah, because it is within the realm of Oral Torah that Bnei Yisrael hold sway over the Torah, and have the ability to delve deeper into it and develop their part in it, which is why G-d said “to part with it- that I cannot bear.”
כתב לך את הדברים האלה כי על פי הדברים האלה כרתי אתך ברית ואת ישראל
“Write these words for yourself, for according to these words have I sealed a covenant with you and Israel.”
Why was Moshe commanded to write these words down—specifically after the sin of the Golden Calf—in the second לחות, the Tablets, rather than in the first?
The Ramban explains that Moshe was commanded to write these words as a new covenant that G-d made with the Jewish people. With G-d’s forgiveness for the sin of the Golden Calf came a new covenant , as the Ramban writes
G-d, blessed be He, had to make with them a covenant on the forgiveness that He extended to them [for their sin with the Golden Calf] and so [Moshe] wrote the forgiveness, and the conditions [on the new covenant].
We see from these words that G-d made stipulated new conditions with his forgiving Bnei Yisrael for this sin, and in forgiving them He renewed His covenant with them.
The main principle of this covenant is the clear knowledge that the Oral Torah was also given to Moshe at Har Sinai, and no one has the right to take the Torah and due with it as he or she pleases. Those who made the Golden Calf were not idol worshippers, rather they merely intended to make a calf, an icon, similar to the Cherubs above the Ark. When Bnei Yisrael fulfilled G-d’s will the Cherubs faced each other, and when they did fulfill G-d’s will the Cherubs faced away from each other. Thus they made the Golden Calf in the image of an ox eating grass. So what was so wrong with what they did? Says the Beis HaLevi, The Cherubs would also have been considered idol worship has they not been commanded to make them.
G-d wanted us to learn this lesson forever, that we can only rely on the words of our sages and do as they command us, and the Oral Torah bears as much credence as the Written Torah. And just as the Written Torah, cannot be studied by heart, so too the Oral Torah (literally “Torah of the heart”) cannot be written. Thus, G-d did not enter a covenant with the Jewish people but for the Oral Torah as the passuk says, “… for according to these words have I sealed a covenant with you and Israel.”
 שמות ל"ד: כ"ז
 גיטין ס' ע"ב
 פרשת בלק
 ברכות ח' ע"א
 נדרים פ"א ע"א
 מגילת סתרים לרבינו יונה
 See תוספות on שבת י"ב ע"א. For further insight see the נעם אלימלך on פרשת בהעלותך.
 פסחים נ' ע"ב
 יומא ט' ע"ב
 מדרש רבה פרשת תנחומא ל"ג ע"א
 פרקי אבות פ"ג:ו'
 חלק ג' קי"ח ע"א
 See also the Ramban in his commentary at the beginning of פרשת תרומה, where he discusses that the dwelling of the Shechina in the mikdash is a continuation of G-d’s presence at Har Sinai at Matan Torah.
 בבא מציעא נ"ט ע"ב
 בבא מציעא פ"ו ע"א
 See דרשות הר"ן דרוש ה' on this point
 הל' טומאת מצורע פרק ב' הלכה ט'
 פרק הנודר מן המבושל. Also brought in ש"ך יו"ד סי' קפ"ט סק"יג
 תהלים נ"ז:ג'
 גיטין ס' ע"ב
 שמות ל"ד: כ"ז
 בבא בתרא צ"ט ע"א