General

Chapter 1: Introduction.

Law 1: Month is lunar; year is solar.
Law 2: Solar year is ~11 days longer than the lunar; when discrepancy accumulates to ~30 days, year is made leap.
Law 3: Moon is not seen for ~1 day before and after the conjunction; first night when the Moon is sighted - Rosh Chodesh; next Rosh Chodesh: if it is sighted on the night of the 30th day - 30th; if not - 31st.
Law 4: Short/full month.
Laws 5-8: Court calculates in a manner resembling the calculations of the astronomers.

Chapter 2: Court procedure.

Laws 1-10: Court procedure.

Chapter 3: Court procedure.

Laws 1-19: Court procedure; messengers.

Chapter 4: Leap Year.

Laws 1-2: Leap year - additional Adar; Pesach (15th of Nisan) must in the spring: not before the day of vernal equinox (Sun enters Aries, see 9:3) and before the next summer solstice.
Laws 3-8: Other reasons for leaping the year; (Succos after the autumnal equinox - not mentioned in Rambam.)
Laws 9-17: Court procedure.