Basics
How to Win at Chess, 10 Golden Rules

Daniel King

Fundamentals for all ages, levels.
Simple Checkmates

A. J. Gillam

Fundamentals for all ages, levels.

 

Tactics
Winning Chess Tactics for Juniors Lou Hayes Fundamental chess problems for the developing player.
Combination Challenge John Hall Combination problems for the intermediate player.

 

Endgame
Endgame Challenge Lou Hayes Fundamental endgame problems for all levels.
Just the Facts! Lev Alburt An effective presentation of endgame principles with something for all levels.