The first volume of this series reviews the mathematical fundamentals of Riemannian geometry, which itself serves as the foundation of spacetime physics. Vector calculus is introduced, and the metric, the curvature, and the torsion are emphasized immediately. Linear algebra then prepares the way for real analysis and manifold theory. For the convenience of the reader, a brief review of algebraic equations, trigonometry, and single-variable calculus is included in the appendix.
