One of the consequences of violation of CP invanance of the physical world is the existence of an electric dipole moment of elementary particles. The renormalization gauge theory of the electroweak and strong interactions developed during the past decade has revealed several possible sources of violation of CP invanance: direct violation of CP invariance in the Lagrangian of the electroweak interactions, spontaneous violation of CP invariance, and violation of CP invariance in the strong interactions described by quantum chromodynamics. The present review is devoted to a discussion of the predictions for the electric dipole moment of the neutron which follow from the various sources of violation of CP invariance in the theory. It includes the theoretical results obtained in the framework of gauge theory during the past decade up to the beginning of 1982. A comparison of the prediction of various gauge models with the experimental measurements of the electric dipole moment will make it possible to gain a better understanding of the nature of violation of CP invariance.