Elementary Differential Geometry, Revised 2nd Edition, Hardback/Barrett (University of California, Los Angeles, California, U.S.A.) O'Neill

Intended for students who have completed the standard first courses in calculus and linear algebra, this edition provides an introduction to the geometry of curves and surfaces. It places emphasis on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.