chapter 1 Algebraic Geometry -- chapter 2 Lie algebras -- chapter 3 Algebraic groups: basic definitions -- chapter 4 Algebraic groups: Lie algebras and representations -- chapter 5 Algebraic groups: Jordan decomposition and applications -- chapter 6 Actions of algebraic groups -- chapter 7 Homogeneous spaces -- chapter 8 Algebraic groups and Lie algebras in characteristic zero -- chapter 9 Reductivity -- chapter 10 Observable subgroups of affine algebraic groups -- chapter 11 Affine homogeneous spaces -- chapter 12 Hilbert’s 14th problem -- chapter 13 Quotients.