180 Years of Invariant Theory

Invariant Theory is a branch of algebra that is more than 180 years old. During these years it came through several periods of rises and falls. Nowadays, it comes through the new period of vigorous developments, flourishing again because of the deep, mutually fruitful links with a number of disciplines (algebraic groups, Lie groups, algebraic geometry, commutative algebra, homological algebra, Galois theory, ring theory, combinatorics, coding theory) and famous mathematical problems (Hilbert's 14th and 13th problems). In fact, Invariant Theory gave birth to some of them (commutative algebra and homological algebra).
The purpose of the talk is to give a survey, intended for the nonexperts, of the main streams and results of this theory, from the beginning to the present time.