Differential Geometry of Curves and Surfaces: A Concise Guide presents traditional material in classicial differential geometry field along with important ideas of Riemannian geometry. The reader is introduced to curves, then to surfaces, and finally to more complex topics. Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels.

The work covers central concepts including curves, surfaces, geodesics, intrinsic geometry, the Aleksandrov global angle comparison theorem, and the celebrated Toponogov Comparison Theorem. This rigorous exposition, with well-motivated topics and many nontrivial and original problems (some with hints and solutions), is ideal for advanced undergraduate and first-year graduate students seeking to enter the fascinating world of geometry.