For beginners in differential geometry, it's essential to start with the fundamentals of curves and surfaces, requiring a solid understanding of calculus and linear algebra. Recommended introductory books include titles available on Amazon, along with free lecture notes by Shifrin that cover key topics such as Gaussian curvature and the Gauss-Bonnet theorem. After grasping the basics, learners can advance to modern differential geometry, which necessitates knowledge of real analysis, metric spaces, and topology. A suggested topology book is also available on Amazon. For further study, Lee's works are recommended, along with Burke's "Applied Differential Geometry," which focuses on numerical methods and includes source codes. Sternberg's "Curvature in Mathematics and Physics" is noted but is not suitable for beginners, as it requires prior knowledge of differential geometry on manifolds.
