Karma and Reincarnation are one of the central concepts of Hinduism. Although it is also a concept that is explored by many Western Philosophies. This article however is restricted to the concept that is discussed in the Indian Scriptures and Indian Philosophies. Karma and re-birth also comprise the core of Indian Philosophies as it is through this that the difficulties in overcoming suffering is measured. The path that needs to be followed in order to attain liberation or freedom from bondage is often by annihilating Karma thereby annihilating Re-birth.
The knowledge about laws of Karma and reincarnation is believed to be first revealed by God to sages who underwent deep and focused meditations. Thus they are considered to be direct revelations by God made to the sages (rishis)
The concept of Karma is simple. Action and Reaction. According to Karma every action we do will have an equal reaction. Therefore if we do good things we may get good in return and if we do bad things then we may get bad returns. However, this Karma is not limited to present human life but also extends itself to upcoming lives of humans. If the deeds that we did in this life were full of evil then our next life will also be full of suffering.
Reincarnation comes as a concept that mainly concerns soul. According to Hinduism soul is immortal. It never dies. It just jumps from one body to another. And this cycle of human birth, death and rebirth (jumping from body to body) is called samsara or reincarnation.
The reason why reincarnation happens is because our soul is on a journey to maturation. In order to evolve to its maturity and finally become one with God, the soul has to go through this cycle of reincarnation until a certain number of times. It is said that when a person dies, the soul moves to a Second Realm where it temporarily stays in some other kind of body and when the time comes for rebirth, the soul moves to earthland and again possess a physical body/form. How the next life will be and how many times one will reincarnate majorly depends on our Karmic Deeds done in this life. It is also said that when a soul completes its number of physical rebirths and reaches maturation it further undergoes a cycle of inner development which eventually makes the soul to dissolve and become one with God.
All of these concepts are deeply explored in the Vedas and Upanishads. Most of the orthodox schools that has Vedas as their foundations also expound upon this concept with their own twists and philosophies. In some philosophy the concept of Karma and Re-birth is accepted however none of them accept God as the being who is responsible for Re-birth or Karma in any way. Philosophies such as Buddhism and Jainism do not accept the existence of God however they do believe in birth and re-birth.
Hence, the concept is widely explored in almost every Indian Philosophy whether they agree with it or disagree with it.