Many books on Indian philosophy refer to the six classic indian systems of philosophy. Surendranath Dasgupta's wonderful book (more about it later) gives a nice listing of them.
The systems are divided into the naastika (atheistic) and asthika (theistic) systems, the main difference being whether a system accepts the authority of vedas or not. The naasthica systems are the Buddhism, and Jainism and the Carvaka system.
The asthika systems are
1. Samkhya: attributed to Kapila: most of the earlier works on the subject are said to be lost
2. Yoga: attributed to Patanjali. The original source is Patanjali Yoga Sutras. They are very close to Samkhya (even Dasgupta says that they are so close that we can call them Samkhya-yoga). I quote from vol#1 page 68
"The general metaphysical position of these two systems with regard to soul, nature, cosmology is almost the same, and the difference lies in this that the Yoga system acknowledges a god (Iswara) as distint from Atman and lays much importance on certain mystical practices (commonly called as Yoga practices) for the achievement of liberation, whereas Samkhya denies the existence Iswara and thinks that sincere philosophic thought and culture are sufficient to produce the true conviction of the truth and thereby bring about liberation."
3. Nyaya 4. Vaiseshika: These two are said to be very close to each other.
5. Mimasa (Purva-Mimamsa)
6. Vedanta (also called as Uttara-mimamsa): The Vedanta-Sutras are written by Badarayana (my guess: Vyasa) are mainly in Brahma-Sutras, which are but a summarized statement of the general view of the Upanishads. The most famous commentary is from the great Sankara of the Advaita system.
More about this later.