This volume is a translation from the Russian of D. A. Suprunenko's book which was published in the Soviet Union in 1972. The translation was edited by K. A. Hirsch. The book gives an account of the classical results on the structure of normal subgroups of the general linear group over a division ring, of Burnside's and Schur's theorems on periodic linear groups, and of the theorem on the normal structure of $SL(n, Z)$ for $n>2$. The theory of solvable, nilpotent, and locally nilpotent linear groups is also discussed.