This volume is a modern exposition of some topics in classical algebraic geometry related to the theory of invariants of finite ordered point sets in projective spaces, Cremona transformations and theta functions. Most of the material can be found in the classical literature, especially, in A. Coble's book «Algebraic geometry and theta functions». Included are discussions of such famous classical constructions as the set of 27 lines on a cubic surface and Kummer surfaces. This is interrelated with such modern topics as geometric quotients, standard tableaux, infinite root systems and their Weyl groups, group representations, moduli spaces of abelian varieties and others.