I'm not qualified to say much about this book, but I think it's excellent and thought it deserved a higher amazon rating. Besides being remarkably clear (much like the cold air of Helgason's home country of Iceland), I think it's a great, wonderful bridge between the original works in Lie theory and the more basic textbook treatments of DG and Lie theory out there (Warner, do Carmo, Lee, ...), many of which are quite good. It is filled with references and citations to original papers (some by the author) and is perhaps more connected to the historical genesis of the subject than other textbooks.
"A great book... a necessary item in any mathematical library." -S.S. Chern
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