Lie Groups (Mathematical Association of America Textbooks)

A novel approach, not expository, but a "learn by doing" text. Chapter 3 on the Tangent Space is explained nicely, leading into the general tangent space on an N-Manifold. In a distant context, "advanced" expositions of general relativity, Wald especially, now becomes clear as to what a "tangent" at a point is, as well as the "tangent space" at that point. All motivated by a simple visual analogy on S2. For someone with enough background in abstract algebraic structures and manifolds, one might wish, occasionally, to have the results stated for the general Lie Group rather than a matrix group, but the end notes on each chapter mostly put this in place.Highly recommended for budding undergraduates anxious for more challenges after the first Linear Algebra semester, and for Physics wanting to get right into the SO3 and SU2 groups. Plenty of very useful analogies and motivations from standard R2 and R3 analysis. The quite extensive use of The Hamiltonian Algebra in developing the topology of S3 and the isomorphism of S3 and SO3, in Chapter 2, feels very modern and right on.

This book does not go deeply into the theory for Lie Groups and Lie Algebras but I have found it a wonderful foundation on the subject from which I now can delve a lot deeper. Frankly, I was getting lost before reading it because, as usual, most of the texts are graduate level or references written more to impress than to teach. In my opinion, reading this book followed by Stillwell's text (Naïve Lie Theory) is all an undergraduate needs to be fully prepared to dive into the theory. Neither requires much more prep than algebra and calculus (maybe a smattering of very little basic topology for Stillwell's). But this book is written by an author whose strategy is to ensure that the student understands the subject, an objective more other authors should keep in mind when writing a text (what's a textbook for, anyway). Written clearly with well-chosen exercises(and answers to some of the exercises)and excellent pertinent examples, it succeeds admirably to meet the goals of that strategy. I sincerely wish more textbooks were written using this problem-oriented approach in which the problems become an integral part of the didactic portion of the text instead of a bunch of after-thoughts at the end of the chapters. I hope that the author has a few more textbooks coming with the same approach.

Great book to read before studying lie algebra... It has many details about different lie groups (the author assumes readers don't know abstract algebra...). The only one problem is that for each section, it is formed by exercises (with a little bit explanations between them); so I also looked up other resources in order to have a better understanding of some definitions.

A rare book which can not download from internet