Fulton/Harris's book on representation theory seems to be the "definitive" introductory text on the subject. But is there perhaps a lower level introduction to the subject? Most of the very first examples in F/H are well beyond my knowledge. Thanks.
2026-04-07 19:02:08.1775588528
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Representation Theory book other than Fulton's
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Etingof's representation theory notes are a standard, they are freely available online. These are pretty terse so they require some work, but they don't assume many prerequisites. I personally like the treatment of representations of groups in Dummit and Foote and would read that before anything else.
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I enjoy Ronald Shaw's Linear Algebra and Group Representations.
It, as the title suggests, introduces a lot of linear algebra and group theory as it goes along. For example, the first two chapters are basically a condensed course (or two) of linear algebra and the third chapter starts by covering a lot of group theory. The later chapters then develop more advanced linear algebra (concerning the orthogonal group, spin group and unitary group) followed by material on multilinear algebra.
All in all it is a thorough introduction to the subject with minimal prerequisites.
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I thought Gordon and Liebeck's book, available free here:
Was pretty nice. And, in a Cuil search, I even found a solution's manual:
http://www.mathematik.uni-kl.de/~taylor/PDF/jamesliebeck.pdf
There is a nice little book on the representation theory of finite groups by Serre, Linear Representations of Finite Groups, ISBN 0-387-90190-6.
Else often books in (abstract) algebra contain at least an introduction of the subject of group representations.