Five lectures on three-dimensional varieties

This article is a reproduction of a course of five lectures delivered in the seminar on algebraic geometry at the Moscow State University. The lectures are devoted to an account of the immense progress that has recently been made in the theory of three-dimensional varieties. Unfortunately these results have been accessible to Soviet mathematicians only in the form of announcements. While these lectures contain a solution of Lüroth's problem (see Lecture 3), their main object is to make extensive use of the Abel–Jacobi mapping for families of curves on three-dimensional varieties.