\"《线性代数群(第2版)(英文版)》介绍了：Apart from some knowledge of Lie algebras, the main prerequisite for these Notes is some familiarity with algebraic geometry. In fact, comparatively little is actually needed. Most of the notions and results frequently used in the Notes are summarized, a few with proofs, in a preliminary Chapter AG. As a basic reference, we take Mumford\'s Notes [14], and have tried to be to some extent self-contained from there. A few further results from algebraic geometry needed on some specific occasions will be recalled （with references） where used. The point of view adopted here is essentially the set theoretic one: varieties are identified with their set of points over an algebraic closure of the groundfield （endowed with the Zariski-topology）, however with some traces of the scheme point of view here and there.\"

\"Introducticn to the First Edition lntIoduction to the Second Edition Conventions and Notation CHAPTER AG-Background Material From Algebraic Geometry 1. Some Topological Notions 2. Some Facts from Field Theory 3. Some Commutative Algebra 4. Sheaves 5. Affine K-Schemes, Prevarieties 6. Products; Varieties 7. Projective and Complete Varieties 8. Rational Functions; Dominant Morphisms 9. Dimension 10. Images and Fibres ofa Morphism 11. k-sift ctures on K-Schemes 12. k-Structures on Varieties 13. Separable points 14. Galois Criteria for Rationality 15. Derivatios and Differentials 16. Tangent Spaces 17. Simple Points 18. Normal Varieties References CHAPTER I-General Notions Associated With Algebraic Groups 1. The Notion of an Algebraic Groups 2.Group Closure; Solvable and Nilpotent Groups 3. The Lie Algebra of an Algebraic Group 4. Jordan Decomposition CHAPTER Ⅱ Homogeneous Spaces 5. Semi-Invariants 6. Homogeneous Spaces 7. Algebraic Groups in Characteristic Zero CHAPTER III Solvable Groups 8. Diagonalizable Groups and Tori 9. Conjugacy Classes and Centralizers of Semi-Simple Elements 10. Connected Solvable Groups CHAPTER IV -Borel Subgroups; Rcduetive Groups 11. Borel Subgroups 12. Cartan Subgroups; Regular Elements 13. The Borel Subgroups Containing a Given Torus 14. Root Systems and Bruhat Decomposition in Reductive Groups CHAPTER V?? Rationality\' Questions 15. Split Solvable Groups and Subgroups 16. Groups over Finite Fields 17. Quotient of a Group by a Lie Subalgebra 18. Caftan Subgroups over the Groundfield. Unirationality. Splitting of Reductive Groups 19. Cartan Subgroups of Solvable Groups 20. lsotropic Reductive Groups 21. Relative Root System and Bruhat Decomposition for Isotropic Reductive Groups 22. Central Isogenies 23. Examples 24. Survey of Some Other Topics A. Classification B. Linear Representations C. Rea\"