This volume of the Encyclopaedia contains two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory. The first part is written by T.A. Springer, a well-known expert in the first mentioned field. He presents a comprehensive survey, which contains numerous sketched proofs and he discusses the particular features of algebraic groups over special fields (finite, local, and global). The authors of Part II - E.B.Vinberg and V.L.Popov - are among the most active researchers in invariant theory. The last 20 years have been a period of vigorous development in this field due to the influence of modern methods from algebraic geometry. This book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.

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I. Linear Algebraic Groups.- II. Invariant Theory.- Author Index.

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Algebraic Geometry IV: Linear Algebraic Groups, Invariant Theory (Encyclopaedia of Mathematical Sciences, Vol. 55)

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