Fulton, Harris "Representation Theory"
Real Analysis, Linear Algebra, and Elementary Topology. No prior knowledge of Lie algebras, Lie groups, or representation theory will be assumed.
- The classical linear groups (real and complex forms)
- Closed subgroups of GL(n) as Lie groups
- Linear algebraic groups and rational representations
- Structure of complex classical groups: maximal torus, roots, adjoint representation, Weyl group
- Highest weight theory for representations of semisimple Lie algebras
- Complete reducibility of representations of semisimple Lie algebras and classical groups