Nasso - some souls the Tzadik can elevate directly; others, the more simple ones, he must first connect to the Avot, and only then to higher worlds. Different kinds of Tzadikim - Kehot, Gershon and Merari; kneged Tzaru'im, Zavim, and Tamei Nefesh, who needed to leave the camp. (from Noam Elimelech)
Likutei Moharan 89 and 90 is very similar to the above theme of Chapter 37 of Tanya, about how a Chisaron of an individual is a chisaron of the Shechinah, which is formed of the 600,000 souls of the Jewish people. This very much parallels what is says in chapter 37 of Tanya:
This inability of one’s divine service to ascend to the Sefirot applies not only where one’s motive for engaging in Torah and mitzvot is actually shelo lishmah (“not for its own sake”), i.e., for some ulterior motive, heaven forbid, in which case one is actually serving himself, not G‑d, and his service surely cannot ascend “to stand before G‑d."
Chapter 40 of Tanya also continues the theme of the previous chapter, and then focuses primarily on the concept of Ahavah and Yirah, and how both together are like the wings of a bird. You need both.
Likutei Moharan 93 - Through the person's pacing in their house, he can resurrect the dead. [People move, while angels and animals are stationary.] Elisha brought the son of the Shunamite woman back to life by pacing. Jacob is truth, truth is Torah, and the 5 books of the Torah are the 5 parts of the lungs. Joseph is the heart, hiddeness. The fire of the heart can burn up the entire body. Through the lungs going back and forth (pacing), they cool off the heat of the heart. Jacob was about to settle down, but then the "heat" of Joseph came upon him. [To be a live human being, a person needs this kind of warmth of the heart related to love and fear.] The human being is a Sefer Torah, and through his paces, he can cool off the fire, which is dinim, and bring back the dead. [This seems to be a reference also to Pinchas/Eliyahu, who cooled off the judgments that were upon the Jewish people.
Likutei Moharan 94: There are times when Hashem cannot be Mashpiah Chesed. Only with the combination of Emunah and Chochmah can the Hashpa'ah of good come to the world. (Same idea as before, but here again, the focus is switched)
Chapter 42 of Tanya is also about Yirah, and how it comes from Moshe and the leaders of Israel in every generation. It also talks about how to acquire this Yirah: by seeking it like someone "digging for a treasure buried in the depths of the earth..." One first acquired Yirah in thought and then one translates it into action. (This similar to the idea of conquering and working the Land)
We see the two levels of love and fear described in Tanya as we compare the previous 4 Sefarim with Sefer Devarim, and also as we compare Moshe to most of the other judges and leaders he had to appoint.
Chapter 43: Moshe was the very embodiment of Koach Mah described in Chapter 43 of Tanya, as he said about himself, "Nachnu Mah?"
Chapter 44, towards the end, is also about the need for each person to do his utmost to know G-d and connect to His greatness, each at his/her level. Va'etchanan, towards the end, contains the Shemah - the mitzvah to love G-d with all one's heart, soul and might.
Chapter 45 is about connecting to the middah of rachamim, mercy, taking pity upon our soul, which had to go from the highest heights to the lowest lows.
Chapter 46 focuses on a way to reach a love of Hashem as follows:
This [way] is: to take to heart the meaning of the verse: "As in water, face answereth to face, so does the heart of man to man." This means that as [in the case of] the likeness and features of the face which a man presents to the water, the same identical nice is reflected back to him from the water, so indeed is also the heart of a man who is loyal in his affection for another person, for this love awakens a loving response for him in the heart of his friend also, cementing their mutual love and loyalty for each other, especially as each sees his friend's love for him. This is Elul! Ani L'Dodi veDodi Li! Reciprocity.
Chapter 47: "In every generation and every day a person is obliged to regard himself as if he had that day come out of Egypt."
Chapter 49 of Tanya is about how our love for Him comes from an appreciation and reflection of all that G-d does for us; His tremendous love for us.
Chapter 50 of Tanya is also about the love of G-d that comes from Gevurah, fire; which derives from intellectual comprehension, related to Binah Ila'ah (Week 51) of G-d's greatness.
Chapter 51 of Tanya is about how Hashem is everywhere, yet the Shechinah is more concentrated in certain parts of the body, like the head:
It is with reference to the flow of all the 613 kinds of powers and vitalities from the concealment of the soul into the body in the process of animating it, that it has been said that the principal dwelling place and abode of this flow of life and of this manifestation is situated entirely in the brains of the head. Therefore they first receive the power and vitality appropriate to them acccording to their disposition and character, namely, ChaBaD (chochmah, binah, da'at) and the faculty of thought, and all that pertains to the brains; and not only this, but also the sum-total of all the streams of vitality flowing to the other organs is also contained and is clothed in the brain that is in the head. It is there that the core and root of the said manifest flow of the light and vitality of the whole soul are to be found. From there a radiation is diffused to all the other organs, each of which receives the power and vitality appropriate to it in accordance with its disposition and character: the faculty of sight reveals itself in the eye, and the faculty of hearing manifests itself in the ear, and so forth. But all the powers flow from the brain, as is known, for therein is located the principal dwelling-place of the whole soul, in its manifest aspect, since the sum-total of the vitality that is diffused from it is revealed there. Only, the [individual] powers of the said general vitality shine forth and are radiated from there into all the organs of the body, much in the same manner as light radiates from the sun and penetrates rooms within rooms. (Even the heart receives vitality from the brain; hence the brain has an intrinsic supremacy over it, as has been explained above. )
In a truly like manner, figuratively speaking, does the blessed En Sof fill all worlds and animate them. And in each world there are creatures without limit or end, myriads upon myriads of various grades of angels and souls,... and so, too, is the abundance of the worlds without end or limit, one higher than the other....
Chapter 52 also appears to be a summary of all of Tanya. About how the way to serve G-d is to be enclothed in His Torah and Mitzvot, primarly through the service of the intellect.
The Tanya also ends with the idea of the beinonim eliciting "female waters," and thereby drawing the light of the Shechinah. This is parallel to the blessings given by Moshe, which are elicited from the behavior and characteristics of each one of the Tribes:
The Alter Rebbe writes that Tanya is like a Neshamah Klali, able to answer the question of every kind of Jew. Copies of the Tanya get corrupted, so it is necessary to (get rid of the manuscripts) and publish an authoritative version.
Likutei Moharan, beginning of Chapter 52 is about the Creation of the world, and how apostates make the mistake of thinking that the world has exists/or must have existed forever (Mechuyav B'Metziut). This is similar to the mistakes made in the generation of Enoch and so forth. He then explains that all the worlds are Nichlalim within the souls of Israel. Once the souls of Israel were introduced, then Hashem was "forced," so to speak, to create the worlds.
The first chapter of Tanya is about understanding the nature of the Tzadik, the rasha, and the beinoni. How in the Tzadik, the bad is mevutal to the good, and how in the rasha, the good is mevutal to the bad. The Tzadik gamur has no longer any bad at all.
Likutei Moharan, second part of Chapter 52 is about how to become a Tzadik and have the whole world dependent on you, and that is through hitbodedut, particularly at night. This way, you break the bad, making it mevutal to the good, until it is "mevutal legamreh."
Toldot is about the struggle between Yaakov and Eisav. Yaakov is from Tikkun and Eisav is from Tohu. Yaakov is pnimi while Eisav is from sovev - he cannot properly absorb Kedushah.