These two books, written in the first half of the last century, cover all aspects of the game, starting with how the pieces move through example games. The opening sections are out-of-date, but this is true of any manual -- opening theory moves too fast.

Lasker's Manual of Chess by Emanuel Lasker • Lasker was World Champion from 1894 to 1921 and an excellent writer. The chapter on position play is particularly good. Lasker was also a philosopher and shares his thinking throughout the book.

The Game of Chess by Siegbert Tarrasch • Tarrasch, Lasker's nemesis at the turn of the last century, was one of the greatest early teachers of the game. The chapters on the endgame and the middlegame are good introductions to the subject.

From Beginner to Intermediate

After you become familiar with the elements of chess, the next step is to apply them to your own games. The books in this category explain the ideas flowing through a complete game.

Logical Chess: Move by Move by Irving Chernev • Most Instructive Games of Chess Ever Played by Irving Chernev • These two books were written in the 1950s/-60s. Almost every chess position has several levels of complexity, where an expert will see one level, a master will see another, and a grandmaster yet another. Chernev had a knack for illuminating the level that is most useful for the average player.

The Search for Chess Perfection by C. J. S. Purdy • Purdy, the first World Champion of correspondence chess, spent his entire life writing about the game. This is the only title of Purdy that I've read, but I'm confident that his other writings are equally valuable.

From Intermediate to Expert

There are many good books for the advanced player. Those listed here are also valuable for the player striving for mastery.

Think Like a Grandmaster by Alexander Kotov • Kotov wrote several titles in the 'Like a Grandmaster' series. This was the first and the most valuable.

Zurich International Chess Tournament, 1953 by David Bronstein • The only tournament book on this list, the Zurich event determined Botvinnik's challenger for the 1954 World Championship title match. Bronstein, who battled Botvinnik to a tie in the 1951 title match, dissected chess knowledge as it was at the middle of the 20th century. It's one of the first books explaining the early theory of the Indian Defenses and of the Soviet School.

The Life and Games of Mikhail Tal by Mikhail Tal • Tal's masterpiece is a mix of autobiography and analysis. World Champion from 1960-1961, Tal had an aggressive, attacking style that is a model for that type of play. Tal's book on his 1960 title match with Botvinnik is another classic worth studying.

The Art of Chess Analysis by Jan Timman • Timman, a Dutch grandmaster who was one of the top players of the 1980s, is a modern writer who knows how to explain what is happening in a modern game.

Secrets of Modern Chess Strategy: Advances Since Nimzowitsch by John Watson • The most recent book on this list, Watson picks up where Nimzovich left off. It is a good introduction to modern chess theory.

Openings

I'm not going to recommend any books on specific openings. There are too many of them! You should look for titles that complement your own opening preferences.

One word of caution - don't believe everything you read in an opening book. They often contain errors in analysis.

Modern Chess Openings: MCO-14 by Nick De Firmian • If you want a general work on openings, try this. Older MCOs also have a certain value.

The Middle Game

Chess Tactics for Advanced Players by Yuri Averbakh • Develops the principles behind tactical operations by dissecting double attacks and combinations. Has hundreds of examples, some complete games, and many exercises to test your knowledge.

The Art of Attack in Chess by Vladimir Vukovic • I haven't read this book myself, but so many good players have recommended it that I'm sure it's valuable.

My System by Aron Nimzovich • Like Steinitz, who explained the positional game as it was understood by the best players at the end of the 19th century, Nimzovich explained positional play as it was understood between World Wars I and II.

The Endgame

I'm not going to recommend anything here either. There are several good books written by great players and any one of them will do. Get at least one title that covers all of the elementary endgames.

Chess History

The more you know about the history of the game, the better you'll play. I don't know why it's true, but it is. Maybe it has something to do with general motivation.

Chess: The History of a Game by Richard Eales • There aren't many titles which cover the history of chess from its origin to recent times. Eales goes up to the early 1980s.