A.D. Alexandrov's contribution to the field of intrinsic geometry was original and very influential. This text is a classic that remains unsurpassed in its clarity and scope. It presents his core material, originally published in Russian in 1948, beginning wth an outline of the main concepts and then exploring other topics, such as general propositions on an intrinsic metric; angles and curvature; existence of a convex polyhedron with prescribed metric; curves on convex surfaces; and the role of specific curvature. This text provides Adefinitive source for the development of intrinsic geometry and is indispensable for graduate students who want a better understanding of this subject.

Basic Concepts and Results. General Propositions about the Intrinsic Metric. Characteristic Properties of the Intrinsic Metric. Angle. Curvature. Existence of a Convex Polyhedron with a Given Metric. Existence of a Closed Convex Surface with a Given Metric. Other Existence Theorems. Curves on Convex Surfaces. Area. The Role of the Specific Curvature. Generalization. Appendix. Basic Facts of Convex Bodies.