This textbook treats Lie groups Lie algebras and their representations in an elementary but
fully rigorous fashion requiring minimal prerequisites. In particular the theory of matrix Lie
groups and their Lie algebras is developed using only linear algebra and more motivation and
intuition for proofs is provided than in most classic texts on the subject. In addition to its
accessible treatment of the basic theory of Lie groups and Lie algebras the book is also
noteworthy for including:a treatment of the Baker-Campbell-Hausdorff formula and its use in
place of the Frobenius theorem to establish deeper results about the relationship between Lie
groups and Lie algebras motivation for the machinery of roots weights and the Weyl group via a
concrete and detailed exposition of the representation theory of sl(3 C) an unconventional
definition of semisimplicity that allows for a rapid development of the structure theory of
semisimple Lie algebras a self-contained construction of the representations of compact groups
independent of Lie-algebraic arguments The second edition of Lie Groups Lie Algebras and
Representations contains many substantial improvements and additions among them: an entirely
new part devoted to the structure and representation theory of compact Lie groups a complete
derivation of the main properties of root systems the construction of finite-dimensional
representations of semisimple Lie algebras has been elaborated a treatment of universal
enveloping algebras including a proof of the Poincaré-Birkhoff-Witt theorem and the existence
of Verma modules complete proofs of the Weyl character formula the Weyl dimension formula and
the Kostant multiplicity formula. Review of the first edition: This
