The original edition of "The Theory of Magnetism" developed the various relevant topics using modern methods adapted for the many-body problem. It presented and taught the fermionic field theory central to Onsager's analysis of the statistical mechanics of the two-dimensional Ising model of magnetism. In its pages the Lieb-Mattis theorems on magnetic ordering of electronic energy levels and on the absence of ferromagnetism in one dimension were restated and proved in a form accessible to students. The exchange mechanism in insulators and the Ruderman-Kittel interaction in metals were some of the innovative topics presented to the reader. Spin waves and their interactions were analyzed in some detail. In this new edition, while retaining much of the material in earlier editions, especially the first chapter, the author has eliminated some of the bulk and added a number of new subjects. Among these are the effects of lowering the dimensionality (exact solutions of some important models in zero and one dimension are exhibited and contrasted with the three-dimensional versions) and the importance of the two-body Coulomb interactions. The reader is introduced to the topic of critical exponents. Quoting a novel theorem by Lieb and exotic band structures, the author re-examines the origins of ferromagnetism. In the presentation, physical principles come first, the mathematics second. Developing the reader's intuition and mastery of the subject takes precedence.