Chess Opening Essentials
"Chess Opening Essentials: The Ideas &Plans Behind ALL Chess Openings" by Stefan Djuric is the highest ranked book on chess openings on Amazon, and was voted Best Chess Book of the Year by the Italian Chess Federation. You won't find a more complete analysis of opening moves anywhere. It goes into great depth on the options for both white and black on every opening.
Silman's Complete Engame Course
When it comes to the endgame--the phase of the game when most of the pieces have been removed, when both players are trying for that last checkmating move--there are not too many books better than "Silman's Complete Endgame Course: From Beginner To Master" by Jeremy Silman. The book is written on a very personal level, introducing the reader to the basic strategies of the endgame, and then building upon them with clear examples.
Fischer's 'Memorable Games'
One of the most controversial chess champions in history was Bobby Fischer, the only American World Chess Champion, and, at age 15, the youngest grand master. In "My 60 Memorable Games," Fischer analyzes 60 of his most famous games, move by move--including the legendary "Game of the Century" played against Donald Byrne when Fischer was 13 years old. The book is a wonderful insight into the mind of a unique individual, and offers terrific advice to chess players as well.
'My System'
One book is absolutely necessary in any chess player's library. In the 1920s, Aron Nimzovich set out to provide a complete guideline on the game of chess. His book, "My System," is still widely regarded as one of the best chess books ever written. Nimzovich laid out clear and concise strategies for nearly every aspect of the game of chess, from the opening to the passed pawn to discovered check, and no player wishing to improve his or her game should pass up "My System."