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 ?