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Course notes (by S. Lichtenstein) with all (corrected) handouts as appendices pdf.
Orthogonal groups pdf.
Jordan decomposition via exercises pdf.
Existence of Jordan decomposition pdf.
Affineness of quotients by normal subgroup schemes pdf.
Quotient formalism pdf.
Grothendieck's theorem on tori pdf.
Conjugacy into a maximal torus pdf.
Dynamic approach to algebraic groups pdf.