Written primarily for students who have completed the standard first courses in calculus and linear algebra, ELEMENTARY DIFFERENTIAL GEOMETRY, REVISED SECOND EDITION, provides an introduction to the geometry of curves and surfaces. The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text. *Fortieth anniversary of publication! Over 36,000 copies sold worldwide *Accessible, practical yet rigorous approach to a complex topic--also suitable for self-study *Extensive update of appendices on Mathematica and Maple software packages *Thorough streamlining of second edition's numbering system *Fuller information on solutions to odd-numbered problems *Additional exercises and hints guide students in using the latest computer modeling tools