Gilmore's treatment of Lie groups and Lie algebras is written in the mathematical language which theoretical physicists should be comfortable with. The notation is very clear, the discussion is nearly flawless and the physical relevance is not omitted, which is for example done in more mathematically oriented books. Very thorough, very readable. Perhaps the best feature of this book is that it aims to convey the theory of Lie algebras and Lie groups to physicists. In doing so, the author is careful to give a very simplistic approach so that one not familiar with the subject can understand it. Not to say that the book is elementary, since it builds rapidly into the far more interesting aspects of Lie Groups. A very good read.