A First Course in Differential Geometry - Surfaces in Euclidean Space

This textbook covers the classical topics of differential geometry of surfaces as studied by Gauss: the definition and geometric meaning of Gaussian curvature, the Theorema Egregium, geodesics, and the Gauss–Bonnet Theorem. It is suitable for upper-level undergraduates and contains plentiful examples and exercises, with solutions to selected problems.