Jyotisha is divided into the three branches of Siddhanta ("Indian astronomy"), Samhita - "mundane astrology", which deals with nationally important but hardly mundane events like wars and earthquakes - and Hora, which is detailed "predictive astrology".
There are sixteen divisional charts, known as Varga. Like Western astrology there are twelve signs of the zodiac, although the two traditions measure these differently. Wikipedia notes "Jyotiṣa uses primarily the sidereal zodiac (in which stars are considered to be the fixed background against which the motion of the planets is measured), whereas most Western astrology uses the tropical zodiac (the motion of the planets is measured against the position of the Sun on the Spring equinox)." Over time the differences have led to some drift - in Jyotisha the placement of the planets is still consistent with the actual zodiac, whereas in Western astrology planets fall into the following sign about two thirds of the time. Which might explain why some people born one sign in Western astrology later end up being another.
Jyotisha can be studied as a subject in some Indian universities.