Aleksei I Kostrikin is currently a Corresponding Member of the USSR Academy of Sciences and holds the Chair in Algebra at Moscow State University. A winner of the USSR Award in Mathematics in 1968. Professor Kostrikin's main research interests are Lie algebras and finite groups.

Yuri I Manin is currently Senior Research Staff Member at the Steklov Institute of the Academy of Sciences of the USSR and Professor of Algebra at Moscow State University.Professor Manin has been awarded the Lenin Prize for work in algebraic geometry and the Brouwer Gold Medal for work in number theory.His research interests

also include differential equations and quantum field theory.

This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the work illustrates the many-sided applications and connections of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metric, the theory of Hilbert polynomials, and projective and affine geometries. Unusual in its extensive use of applications in physics to clarify each topic, this comprehensice volume should be of particular interest to advanced undergraduates and graduates in mathematics and physics, and to lecturers in linear and multilinear algebra, linear programming and quantum mechanics.