Besides the basic definitions and examples, you will find a concise description of the vocabulary needed to talk about linear algebraic groups over fields that are not algebraically closed in T. A. Springer's article titled Reductive Groups, which appears in Part I of Automorphic Forms, Representaions, and L-Functions (Proceedings of a conference in Corvallis), A.Borel and W.Casselman (editors), AMS, 1979.
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