This Handbook of Mathematics is a diamond in the rough.
(1) It is the only handbook of mathematics that I know of that includes advanced topics like algebraic topology, category theory, advanced complex analysis, and differential geometry on manifolds, . It also includes proper surveys of abstract algebra and general topology, and decent treatments of logic and set theory, well beyond the merely introductory material that is found in other handbooks of mathematics. Many other subtopics can only be found here, like affine, projective and hyperbolic geometry.
(2) It has many figures illustrating the concepts visually. This is especially useful in the more abstract branches of geometry.
(3) Theorems often have a sketch of their proof.
(1) This is the first edition of this handbook so it has the inevitable associated drawbacks. The organisation of the material is unorthodox. Other handbooks tend to start with the most elementary material and try to present increasingly complex material. This handbook does that, but only within each chapter. For example, the chapter on differential calculus comes after the chapter on abstract algebra. But within the chapter of abstract algebra, the author starts with the simplest material (groups), and proceeds to more complex topics (like rings, modules, and Galois theory). I don't know if it is possible to present all this advanced material any other way, but there are still issues with the organization that need improvement, like unnecessarily dividing complex analysis in two chapters and repeating some of the material in the second chapter.
(2) The book's English has traces of the French language. The author's first language is French, not English. What ends up happening is that, sometimes, the wording of a sentence sounds a bit convoluted because the sentence structure makes more sense in French. But this is a minor complaint. You can preview significant portions of the book on Google Books and check the writing style for yourself.
Overall, I think this is a very good handbook. It has the same core topics found in other handbooks of mathematics, but the inclusion of advanced mathematics, and the treatment throughout from the perspective of pure mathematics, makes it uniquely valuable. The only reason I give it 4.5 stars is due to the inevitable imperfections associated with a first edition.
The book consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII .Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.