Alexandrov's contribution to the field of intrinsic geometry was both original and extremely influential. This volume consists of an original core of classic material, originally published in Russian in 1948, with additional supplementary material making it of particular current interest. It begins with an outline of the main concepts and results and then covers topics including general propositions on an intrinsic metric; characteristic properties of the intrinsic metric of a convex surface; angles and curvature; existence of a convex polyhedron with prescribed metric; curves on convex surfaces and the role of specific curvature. This book provides definitive sources for the development of intrinsic geometry. A classic in the field that remains unsurpassed in its clarity and scope, this text would be of great value to graduate students seeking a better understanding of this area of geometry.