General Relativity for Mathematicians - Part I

These notes cover the first part of a course of the same title taught by Filippo Fila-Robattino and Manuel Tecchiolli at the University of Zurich in the Winter Semester of 2025. Topics include variational principles in classical mechanics, special relativity, smooth manifolds and tensor calculus, connections and curvature, geodesic motion, and the derivation of Einstein's equations from the Einstein-Hilbert action. The treatment is aimed at a mathematical audience, combining physical motivation with precise definitions, detailed proofs, and explicit calculations.