The word Hindu originally meant people living on the banks of the river Sindhu. Now it has religious-cum-philosophical connotations. The roots of Hindu Philosophy are the ideas of the Vedas. The Vedas are called Shruti or `that which is heard' and are regarded as revelations to sages passed down orally to disciples and students. Such ideas led to the Samkhya system of philosophy, which is astik (Theist), rational and systematic in its approach. The sage Kapila of 7th century BC is considered to be its founder.
Yoga is a system complementary to Samkhya, dealing with the practical attainment of liberation from worldly ties. Together the two systems are referred to as SamkhyaYoga. Vedanta refers to the 108 Upanishads which are philosophical musings of the Vedas about the Cause of Creation, Being, Cosmos and so on. Prominent exponents of Vedanta are Shankaracharya and Ramanuja. In contrast, Charvaka or Lokayata philosophy is a Nastin (Atheist), materialist system, which rejects Shrutis, deities, and even the idea of re-incarnation.
Vaisheshika philosophy has a scientific rather than a metaphysical approach and believes that the world is made up of innumerable but distinct (vishesha) particles. Nyaya is a complementary philosophy trying to arrive at `nyaya' or knowledge, which is `just', or `right'. Bhagavat-Gita, a part of the epic Mahabharata, expounds the synthesis of three yogas or ways of attaining union with the Supreme Self, Gyana-yoga (union through knowledge), Bhakti-yoga (union through devotion) and Karma-yoga (union through action).
In relatively later times, Chaitanyadev, Rammohun Roy and Ramkrishna Paramahamsa have enriched Hindu philosophy in their own ways.