Liberation (Self-realization, Mukti, Moksha, Nirvana)

Liberation (also known as Self-realization, Mukti, Moksha, Nirvana etc.) refers to achieving a state when one realizes that everything including himself/herself is Brahm. In that state, one becomes free from Maya. In that state, one goes beyond the sensory perceptions and changing mental states to attain permanent bliss.

Reference Verses in Gita

2.55 - 2.61 Krishna tells Arjun how a liberated person lives and behaves.

Maya

Maya is the process of superimposition by which worldly objects are perceived in the omnipresent Brahm. It is a result of Avidya (ignorance). When one gets liberated, Maya is vanished.

To understand this, consider the process of mirage, when water is perceived in the desert. Another example often used in Vedantic literature is that of a man looking at a rope and thinking of it as a snake.

What we see around us (this world) is not an absolute reality, but a perception by the five senses.

You can argue that even if what you are seeing is an illusion, how come every one also sees the same illusion! How come both you and your friend see exactly the same room, the same chair and the same colors, if they are not real? The short answer is that even your friend (and all that he/she is saying and thinking) is just in your mind.

Soul (Atma, Atman)

Soul (Atma in Hindi, Atman in Sanskrit) is just another name for Brahm, often used in the context of being present inside living beings.

I don't think there is a one-to-one mapping between Atma and body. It is not appropriate to say there is "one" soul inside every body. This is like saying there is "one" gold inside every gold bangle (gold is like Brahm/Atma, gold bangle is like the body). A more appropriate way to say this would be,"body is made of Atma". Hence, there cannot be a one-to-one transfer of the soul from an old body to a single new body after death.

There is also a colloquial usage of the term "soul" which refers to the integrity or the conscience of a person (as in "selling one's soul"). This seems to stem from the above mentioned belief that there is "one" soul inside every person, that guides him on the right path. I think this is a simplistic way of looking at soul and perhaps the root of much confusion. Decisions and emotions are controlled by brain and mind; soul is simply the underlying building block that makes the whole living being, including his body/brain/mind.