We've had a suggestion from Chris Rogers for further reading for people new to the subject. He says that John Hull's book "Options, Futures and other Derivative Securities" is a good accessible introduction to the area.

Also, Chris answered Vaibhav's question: Yes, a derivative can have a value of zero. A down-and-out option will have zero value once the price of the underlying asset falls below a specified threshold. Also an interest-rate swap could have zero value at inception, where one party swaps floating interest payments for payments at a
fixed rate calculated to make the two payment streams exchanged of
equal value.