For those looking to build a solid foundation in Riemannian Geometry, several recommended resources can enhance understanding and provide necessary mathematical rigor. Manfredo P. Do Carmo's "Riemannian Geometry" is suggested for its logical presentation, though it may present challenges with problem sets for those lacking prior knowledge. A more accessible starting point is his "Differential Geometry of Curves and Surfaces," which serves as a prequel and may better prepare learners. John Lee's books are also noted for their popularity among self-learners, particularly "Introduction to Smooth Manifolds" and "Riemannian Manifolds." For a strong grasp of multivariable calculus, Spivak's "Calculus on Manifolds" is highly recommended as it lays the groundwork for further studies in differential and Riemannian geometry. Additionally, a practical resource featuring numerical algorithms related to surface geometry is available, providing source codes and examples for hands-on learning.
