The Mishna Torah chapters for the week of Yom Kippur (usually for Erev Yom Kippur or Yom Kippur itself) include Hilchot Teshuvah, the laws of repentance.
Shavuot is Chag HaBikurim. The Torah reading for the chag (when it doesn't fall on Shabbat) starts with the laws of Bechorot. The Mishnayot chapters for Shavuot and the days leading up to it are the ones for Bechorot. Shavuot is also the culmination of the redemption process that began on Pessach, where we were called, Beni Bechori, Yisrael. The remaining Mishnah chapters relate to Erchin, which is about offering ones' "worth" as a donation to the Temple; it is a kind of "giving over" similar to what happened at Mount Sinai, when the Jewish people said, Na'aseh veNishmah. Erchin is also a topic in the Torah reading of Bechukotai, at the very end of Vayikrah, always read before Shavuot).
Temura is about someone who tries to switch the holiness of one animal for that of another. When doing so, while the first one does not lose its holiness, the second now becomes holy is as well. This represents an important lesson for the week following Shavuot and the Shiva Yemei Miluim. After acquiring the Torah and experiencing such a high, we now switch back to the mundane, and the pull of the Klipot is much stronger. The Torah comes to teach us that during this switch, not only does the "first animal" (one's earlier Shavuot state) not lose its holiness, the "second animal" (this new stage, of involvement in the world) becomes holy as well.