General Methods and Ideas.- Symmetric Functions.- Theory of Algebraic Forms.- Lie Algebras and lie Groups.- Tensor Algebra.- Semisimple Algebras.- Algebraic Groups.- Group Representations.- Tensor Symmetry.- Semisimple Lie Groups and Algebras.- Invariants.- Tableaux.- Standard Monomials.- Hilbert Theory.- Binary Forms.
From the reviews:
"Lie Groups ... is a spectacular book. ... is a pleasure to read, and the topics covered are perfectly chosen. ... preliminary remarks set the stage perfectly for what follows, smoothing out what might otherwise have been rougher patches (certainly to the neophyte). And the whole book is written in this way, making for remarkable accessibility. Given that it is published in Springer's Universitext series ... Lie Groups: An Approach through Invariants and Representations is probably the best book I've ever seen for this purpose." (Michael Berg, MAA Online, May, 2007)
"The author draws on his long involvement with 'modern' invariant theory to provide an extensive account of the subject, thoroughly integrated with Lie theory. ... Procesi's book will be a valuable resource for anyone coming into contact with invariant theory and its connections with representation theory. Nowhere else is so much of the essential material brought together under one roof." (James E. Humphreys, Mathematical Reviews, Issue 2007 j)
"Procesi's book touches on almost all topics ... with a great deal of emphasis on invariant theory. ... the author has attempted to paint a huge canvas and has succeeded in doing it. ... the book gives a wealth of information about invariant theory, both classical and modern, which is difficult to get from other sources. I recommend it strongly for any reader who wants to learn, in depth, about Lie groups, their representations and invariants." (V. S. Varadarajan, Bulletin of the American Mathematical Society, Vol. 45 (4), October, 2008)
"Lie theory ... is one of the central areas in mathematics and mathematical physics. ... The chapters ... can be taken as the subject of an entire, largely independent graduate course. ... All in all, this unique textbook, combing invariant theory and Lie theory in a very natural way, refers to virtually every (classical and modern) aspect of this deep interrelation ... . The author's effort at providing such a rich source of insight must be seen as being highly welcome, rewarding, valuable ... ." (Werner Kleinert, Zentralblatt MATH, Vol. 1154, 2009)