Irving Chernev's "Logical Chess Move by Move", "The Most Instructive Games of Chess Ever Played" and "Best Endings of Capablanca" - the extremely anal-retentive chess historian/writer Edward Winter stated the last one is Chernev's best book, no slight compliment coming from someone as fussy as Winter
"My System" by Nimzovitch, you may not grok every chapter in it ASAP but you will eventually if you keep on playing.
AND don't overlook various resources here such as Tactics Trainer and Chess Mentor, both very useful and instructive.
Look around for used PBs at amazon. GOOD LUCK!
I was wondering if anyone could point me in the direction of a good book to start out with... I've been playing for quite some time, and have a good understanding of this game. I want a deeper understanding of this game. Can anyone help me?? Please... :)