Taylor D.E. The Geometry of the Classical Groups

Berlin: Heldermann Verlag, 1992. — 239 p.The author starts with the introduction of vector spaces, sesquilinear forms, and then studies the classical groups - special linear, symplectic, unitary and orthogonal groups - along the lines of E. Artin. Emphasis is placed on the "building" of the groups and their corresponding BN-pairs. Symplectic groups, unitary groups, orthogonal groups, and the Klein correspondance are thoroughly treated in individual chapters, each offering an abundance of exercises for deepening the understanding.