"A free translation, with additional material, of a book and a set of notes, both published originally in Portuguese."

Includes bibliographical references and index.

1. Curves: Parametrized Curves. 2. Regular Surfaces: Regular Surfaces; Inverse Images of Regular Values. 3. Geometry of the Gauss Map: Definition of the Gauss Map and Its Fundamental Properties. 4. Intrinsic Geometry of Surfaces: Isometrics; Conformal Maps. 5. Global Differential Geometry: Rigidity of the Sphere.

This volume covers local as well as global differential geometry of curves and surfaces. *Makes extensive use of elementary linear algebra - with emphasis on basic geometrical facts rather than on machinery or random details. *Stresses the basic ideas of differential geometry - regular surfaces, the Gauss map, covariant derivatives. *Includes a large number of fully-worked examples.