Published in English for the first time, this is the second part of a two volume set containing an extensive range of the most important papers by the geometer A.D. Alexandrov.

Progress in geometry in recent decades correlates with the resurrection of the synthetic methods of geometry and brings the ideas of Alexandrov once again into focus. This text is a classic that remains unsurpassed in its clarity and scope.

BASIC CONCEPTS AND RESULTSThe General Concept of Intrinsic Geometry and Its ProblemsGaussian Intrinsic GeometryA Polyhedral MetricDevelopmentPassage from Polyhedra to Arbitrary SurfacesA Manifold with Intrinsic MetricBasic Concepts of Intrinsic GeometryCurvatureCharacteristic Properties
of the Intrinsic Metric of a Convex SurfaceSome Special Features of Intrinsic GeometryTheorems of Intrinsic Geometry of
Convex SurfacesGENERAL PROPOSITIONS ABOUT THE INTRINSIC METRICGeneral Theorems on Rectifiable CurvesGeneral Theorems on
Shortest ArcsNonoverlapping Condition for Shortest ArcsA Convex NeighborhoodGeneral Properties of Convex DomainsTriangulationCHARACTERISTIC PROPERTIES OF THE INTRINSIC METRICConvergence of Metrics of Convergent Convex SurfacesConvexity Condition for a Polyhedral MetricConvexity Condition for the Metric of a Convex SurfaceConsequences of the Convexity ConditionANGLEGeneral Theorems on Addition of AnglesTheorems on Addition of Angles on Convex SurfacesThe Angle of a Sector Bounded by Shortest ArcsOn Convergence of AnglesThe Tangent ConeThe Spatial Meaning of the Angle Between Shortest ArcsCURVATUREIntrinsic CurvatureArea of the Spherical ImageGeneralization of the Gauss TheoremCurvature of Borel SetsSet of Directions in Which It Is Impossible to Draw a Shortest ArcCurvature as a Measure of Non-Euclidicity of SpaceEXISTENCE OF A CONVEX POLYHEDRON WITH A GIVEN METRICOn Determination of a Metric from a DevelopmentThe Idea of the Proof of the Realization TheoremSmall Deformations of a PolyhedronDeformation of a Convex Polyhedral AngleRigidity TheoremRealizability of the Metrics That Are Close to the Realized MetricsSmooth Passage from a Given Metric to a Realizable MetricProof of the Realization TheoremEXISTENCE OF A CLOSED CONVEX SURFACE WITH A
GIVEN METRICThe Result and the Method of ProofThe Main Lemma on Convex TrianglesConsequences of the Main Lemma on Convex TrianglesThe Complete Angle at a PointCurvature and Two Related EstimatesApproximation of a Metric of Positive CurvatureRealization of a Metric of Positive Curvature Given on the
SphereOTHER EXISTENCE THEOREMSGlueing TheoremApplication of
the Glueing Theorem to the Realization TheoremsRealizability of a Complete Metric of Positive CurvatureManifolds on Which a Metric of Positive Curvature Can Be GivenUniqueness of a Convex SurfaceVarious Definitions of a Metric of Positive CurvatureCURVES ON CONVEX SURFACESThe Direction of a CurveThe Swerve of a CurveGeneral Glueing TheoremConvex DomainsQuasigeodesicsA CircleAREAThe Intrinsic Definition of AreaThe Extrinsic-Geometric Meaning of AreaExtremal Properties of Pyramids and ConesTHE ROLE OF SPECIFIC CURVATUREIntrinsic Geometry of a SurfaceIntrinsic Geometry of a Surface of Bounded Specific CurvatureShape of a Convex Surface in Dependence on Its CurvatureGENERALIZATIONConvex Sur