Resources to learn about the P vs. NP problem I was recently reminded about the $\mathsf{P}$ vs. $\mathsf{NP}$ problem as explained by Stephen A. Cook on Clay Mathematics Institute.

It has piqued my interest and I would like to learn more about it. The first step would be gaining a deeper understanding of the problem and an understanding of the area in general.

Can you recommend any books or other resources where I can learn more about the problem?
It's good to see a fellow undergrad in pursue of this great problem, with such an enthusiasm. Allow me to offer you a piece of advice from my own experiences.

$ P \neq NP $ is a very interesting problem. The implications of the answer are immense, especially in the case that the two classes are equal. The reward is great in many levels, from the altruistic scientific one to the materialistic money award. That leads many young people that encounter the problem in trying to solve it, with no or limited knowledge about it. 

Perhaps most theory students go through that phase. You will have an idea and think it is right, but it is almost certain that you are wrong. Some people never get through that phase and embarrass themselves by being too stubborn to admit their errors.

In FOCS 2010, Rahul Santhanam compared the $ P \neq NP $ question to a mythical monster. It would take many sacrifices and courage to even try to defeat this monster. After all, it may be the most difficult problem ever. To have a fighting chance, you will have to study a lot about this problem and complexity in general. You'll never know what the "monster's weakness" will be. 

So my advice is this: Take your time in knowing the problem. Every time you figure out a solution, assume you are wrong somehow and try to find the problem with it. That way you'll learn much.

As for references, I would recommend Sipser's book as well. After finishing it, I would recommend "Computational Complexity:A modern approach" by Arora and Barak, a more complexity-oriented book, that requires a good understanding of the concept of computation.