How should I prove the correctness of algorithm ?

While solving problem I used to think for an idea,then I will code it.
But i never thought about the correctness of algorithm.
What is correctness of algorithm ?
How should I prove it?
Is it necessary for every problem.Any one give me link or examples how to prove the correctness of algorithm.

You can refer to the MIT - open courseware(OCW) 42.
It is based on proofs

MIT is Ok.

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