The Six Darshanas
The darshanas are philosophical systems meant to be complement rather than compete with each other. They incorporate philosophy, theology, psychology, philology, physics, meditation and other esoteric spiritual practices. Together they form the six schools of orthodox Hindu thought that had evolved by the end of the 4th century, but only a few of them are still active in modern Hinduism, since they developed out of each other, tending to make previous darshanas somewhat obsolete. They are traditionally arranged in three pairs, each divided into sub-schools.
Nyaya and Vaisheshika cover logic and physical principles.
Sankhya and Yoga deal with Hindu metaphysics and psycho-physical exercises.
Purva-Mimamsa and Vedanta. Purva-Mimamsa explores the theology of Vedic sacrificial ritual. Vedanta (originally called Uttara-Mimamsa) is the complex system of philosophy that rules most of Hindu religious thought today, both within and outside of India.