This is an introductory course on Riemannian Geometry for graduate students in pure/applied mathematics or physics, and advanced undergraduate students who are strongly interested in geometry and topology. The goal of the course is to equip students with essential knowledge on Riemannian Geometry for research or further studies in related fields such as Geometric Analysis, General Relativity, etc. Topics will include Gauss's Theorema Egregium, Riemannian manifolds, parallel transport and holonomy, geodesics, curvature tensors, Jacobi fields, etc. If time permits, contemporary topics such as geometric flows will be covered at the end of the course.