This is a book on Lie groups and Lie algebras intended to serve as a textbook for a two-semester graduate course, or a very intensive one-semester course. The topics covered, as can be seen from the table of contents, are the standard and expected ones, but there are a few very important features that set this book apart and make it a very good choice.
First, the book is very readable for, instead of emphasizing the technical details, the ideas of the proofs are insisted upon. Secondly, every chapter ends with an extensive list of well-chosen exercises. Thirdly, there is a very good bibliography enclosed, as well as an Overview of the literature including the basic textbooks, as well as monographs. Moreover, the book even has a Sample syllabus.
As expected, there are some prerequisites necessary for readers of this text, but they are kept to a minimum: basics of topology, abstract algebra, differential geometry, homological algebra.
I strongly recommend this book as a possible selection for graduate course(s), as well as for independent study, or individual reading.
The book also has a web page: http://www.math.sunysb.edu/~kirillov/liegroups/
Mihaela Poplicher is an associate professor of mathematics at the University of Cincinnati. Her research interests include functional analysis, harmonic analysis, and complex analysis. She is also interested in the teaching of mathematics. Her email address is Mihaela.Poplicher@uc.edu.
2. Lie groups: Basic definitions
3. Lie groups and Lie algebras
4. Representations of Lie groups and Lie algebras
5. Structure theory of Lie algebras
6. Complex Semisimple Lie algebras
7. Root systems
8. Representations of Semisimple Lie Algebras
Overview of the literature
A. Root systems and simple Lie algebras
B. Sample syllabus
List of notation