170 years of invariant theory

Invariant Theory emerged about 170 years ago as a study of polynomials which are transformed in a prescribed way under nondegenerate linear transformations of variables. This theory went through several periods of rises and falls and nowadays it is flourishing again mainly because of deep, mutually fruitful connections with a number of disciplines (algebraic groups, Lie groups, algebraic geometry, commutative algebra, homological algebra, Galois theory, ring theory, combinatorics and coding theory). The talk is designed as a survey, intended for nonspecialists, of the main streams and results of Invariant Theory, from the beginning to the present time.