These lectures were delivered to the high school students at the School – seminar «Nonlinear Days for Youth in Saratov – 2012» in October 2012. They present the two ways of historical investigation of symmetry. The first way is self-similarity, i.e. invariance at dimension scale changing. In a more general way the term «scaling» is used, meaning the existence of power-law correlation between some variable and variables x1, ...xn: y = Axα1...xαn1 (self-similarity) appearing in various fields of science and culture. G.I. Barenblatt indicates that scaling laws never appear by accident.
