What are some good books to study mathematical logic?

I am a CS student and have a very poor understanding of this field of mathematics. I don't properly know the difference in between symbolic logic, first order logic, propositional calculus, model theory and lambda calculus. But, I want to start studying logic formally from the very basic.

I'd like to be able to solve some seemingly simple puzzles like the Lady and the Tiger, or Knights and Knaves. I'd like to be able to get to a level where I'd be able to solve these questions easily, with the approach of mathematical logic rather than intuitive heuristics.

Can someone guide me as to what books are good, where I can begin and what are some more advanced books and topics I can work up to later on ?

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I actually solved the knights and the knaves using logic.. It was glorious xD

Here is a nice introduction:
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/discrete_ch10.pdf

A book I am using is in the for dummies series..called logic for dummies.

the knight and the knaves can be solved after reading that PDF alone, those are very basic, just scratching the surface of logic.

Can you tell me about some of the things that lie beyond the surface?

Can you tell me about some of the things that lie beyond the surface?
I really dont know too much.. I have only reached so far as to study proofs using logic. Set notation can be expressed logically..I think logic is central to proving some of the more abstract math theorems. Computing uses logic, software etc..

Any equation can also be called a proposition...a logical statement.. Its one of the things about mathematics I am seeing so far, there are many ways of seeing one concept..at least, how I feel.

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