An Introduction To Lie Groups And Lie Algebras 1st Edition Alexander Kirillov by Alexander Kirillov, Jr. 9780521889698, 9780511423192, 0521889693, 0511423195 instant download after payment.

this is a wickedly good book. it's concise (yeah!) and it's well written. it misses out on lots of stuff (spin representations, etc..). but once you read this book you will have the formalism down pat, and then everything else becomes easy.
if you put in the hours to read this book cover to cover -- like sitting down for 3 days straight 8 hours a day, then will learn the stuff. if you don't persevere and get overwhelmed with the stuff that is not clear at the beginning, then you will probably chuck it out the window.
lie groups and lie algebras in 200 pages done in an elegant way that doesn't look like lecture notes cobbled together is pretty impressive.

This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Lie theory, in its own right, has become regarded as a classical branch of mathematics. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. The book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.

Exposition follows the style of famous Serre's textbook on Lie algebras: we tried to make the book more readable by stressing ideas of the proofs rather than technical details. In many cases, details of the proofs are given in exercises (always providing sufficient hints so that good students should have no difficulty completing the proof). In some cases, technical proofs are omitted altogether; for example, we do not give proofs of Engel's or Poincare–Birkhoff–Witt theorems, instead providing an outline of the proof. Of course, in such cases we give references to books containing full proofs.