Chapter 1 The Euler Characteristic and Related Topics

Chapter 2 Selected Topics in Elementary Differential Geometry

Chapter 3 The Isoperimetric Inequality and Related Inequalities

Chapter 4 The Elementary Concept of Area and Volume

Chapter 5 Introduction

Chapter 6 Differential Geometry of Surfaces in the Small

Chapter 7 Some General Remarks on Closed Surfaces in Differential Geometry

Chapter 8 The Total Curvature (Curvatura Inteqra) of a Closed Surface with Riemannian Metric and Poincaré’s Theorem on the Singularities of Fields of Line Elements

Chapter 9 Hadamard’s Characterization of the Ovaloids

Chapter 10 Closed Surfaces with Constant Gauss Curvature (Hilbert’s Method) — Generalizations and Problems — General Remarks on Weinqarten Surfaces

Chapter 12 Simple Closed Surfaces (of Arbitrary Genus) with Constant Mean Curvature — Generalizations

Chapter 13 The Congruence Theorem for Ovaloids

Chapter 14 Singularities of Surfaces with Constant Negative Gauss Curvature