Megillah, Chapter 3, Mishnah 6. The Mishnah continues to list the Torah readings for the special days of the calendar year, detailing what is read on each and every occasion.
The readings for the festivals and special days:
On Chanukah - "BaNesi'im": During the days of Chanukah we read the portion of the offerings of the princes who brought them at the dedication of the Mishkan, found in Parashas Naso.
On Purim - "Vayavo Amalek": The passage at the end of Parashas Beshalach, which tells of the war with Amalek.
On Rosh Chodesh: Here the reading is somewhat broader - we read the portion of the daily Tamid offering, together with the portion of the Shabbos additional offering, and after them the portion of Rosh Chodesh.
At the ma'amados: When all of Israel was divided into groups that would accompany the offerings in Jerusalem, they would read the account of the seven days of Creation.
On fast days: They would read the tochachah - the curses in the book of Vayikra, from Parashas Acharei Mos. It is worth noting that we do not follow this practice today; instead we read the portion of the golden calf.
The law of reading the tochachah without interruption:
Whenever the tochachah is read, we do not break in the middle of it to add another aliyah; rather, one person reads the whole of it. The reason: so that he can open and close on a positive note - with the verses before the tochachah and the verses after it - and not be forced to begin his aliyah or end it with something negative, as would happen if we were to break in the middle.
The reading on Monday, Thursday and Shabbos Minchah:
On Monday and Thursday, and likewise at Minchah on Shabbos, we read from the order of that week's parashah - from the reading of Shabbos itself, except that we read only its first portion. And this reading is not deducted from the Shabbos reading: one should not say that since we already read up to "sheni" during the week, on Shabbos we should begin from "sheni" onward. On Shabbos we read the entire parashah from its beginning.
The source of the law:
This entire principle - that on every occasion we read from the portion relevant to that occasion - is derived from the verse "Vayedaber Moshe el bnei Yisrael" - "And Moshe spoke to the children of Israel." From here we learn that there is a mitzvah to read about the subject of each festival at its proper time: on Pesach about Pesach, on Sukkos about Sukkos, and so on.
In summary: In this Mishnah we learned the Torah readings of the special days - the princes on Chanukah, "Vayavo Amalek" on Purim, the portions of the Tamid and Rosh Chodesh on Rosh Chodesh, the account of Creation at the ma'amados, and the tochachah on fast days; the law that we do not break in the middle of the tochachah, so as to open and close on a positive note; the relationship between the reading on Monday, Thursday and Shabbos Minchah and the Shabbos reading itself; and the source for reading about each occasion at its proper time.