Helps students see mathematics as an organic whole by focusing on the geometric while presenting viewpoints and methods that require a general understanding and unification of previous mathematical backgrounds. Develops basic metric topological methods and algebraic needs. Reviews vector character of Euclidean n-space and familiar facts from linear algebra; concepts relevant to convex body theory; and the affine character of the space and the analogy between linear and affine concepts. Explains how n-dimensional convex bodies and surfaces of Euclidean n-spaces are identified and how basic properties are established, showing how to express fundamental concepts accurately and how to verify intuitive relations analytically in space of general dimensions. Also contains a selection of standard fundamental theorems. Excellent preparation for further study of convexity theory, optimization theory, or basic analysis, topology, and geometry.