This self-contained text takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces. It develops students geometric intuition through interactive computer graphics applets supported by sound theory. This edition includes more exercises and project ideas, reorganized material on the GaussBonnet theorem, and a new chapter on curves and surfaces in Rn. New sections cover applications to cartography and problems in spherical and hyperbolic geometry.