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 Gauss-Bonnet theorem, and a new chapter on curves and surfaces in Rn. New sections cover applications to cartography and problems in spherical and hyperbolic geometry.

Thomas F. Banchoff is a geometer and a professor at Brown University. Dr. Banchoff was president of the Mathematical Association of America (MAA) from 1999 to 2000. He has published numerous papers in a variety of journals and has been the recipient of many honors, including the MAA's Deborah and Franklin Tepper Haimo Award and Brown's Teaching with Technology Award. He is the author of several books, including Linear Algebra Through Geometry with John Wermer and Beyond the Third Dimension.

Stephen T. Lovett is an associate professor of mathematics at Wheaton College. Dr. Lovett has taught introductory courses on differential geometry for many years, including at Eastern Nazarene College. He has given many talks over the past several years on differential and algebraic geometry as well as cryptography. In 2015, he was awarded Wheaton's Senior Scholarship Faculty Award. He is the author of Abstract Algebra: Structures and Applications and Differential Geometry of Manifolds.

Plane Curves: Local Properties. Plane Curves: Global Properties. Curves in Space: Local Properties. Curves in Space: Global Properties. Regular Surfaces. The First and Second Fundamental Forms. The Fundamental Equations of Surfaces. The Gauss-Bonnet Theorem and Geometry of Geodesics. Curves and Surfaces in n-Dimensional Euclidean Space. Appendix.