In this chapter we put together an overview of the literature and some suggestions for further reading. The list is divided into three sections: textbooks (books suitable for readers just learning the theory), monographs (books that provide detailed coverage but which still can be classified as “core” theory of Lie groups and Lie algebras) and “Further reading”. Needless to say, this division is rather arbitrary and should not be taken too seriously.

Basic textbooks

There is a large number of textbooks on Lie groups and Lie algebras. Below we list some standard references which can be used either to complement the current book or to replace it.

Basic theory of Lie groups (subgroups, exponential map, etc.) can be found in any good book on differential geometry, such as Spivak or Warner. For more complete coverage, including discussion of representation theory, the classic references are Bröcker and tom Dieck or the book by Fulton and Harris. Other notable books in this category include Varadarajan, Onishchik and Vinberg. The latest (and highly recommended) additions to this list are Bump, Sepanski and Procesi. Each of these books has its own strengths and weaknesses; we suggest that the reader looks at them to choose the book which best matches his tastes.