This text for advanced undergraduates and graduate students examines problems concerning convex sets in real Euclidean spaces of 2 or 3 dimensions. It illustrates the different ways in which convexity can enter into the formulation as the solution to different problems in these spaces. 1957 edition.

This account of convexity includes the basic properties of convex sets in Euclidean space and their applications, the theory of convex functions and an outline of the results of transformations and combinations of convex sets. It will be useful for those concerned with the many applications of convexity in economics, the theory of games, the theory of functions, topology, geometry and the theory of numbers.