Textbook in PDF format This book is unique in that, while employing the language of differential geometry, it systematically introduces all the essential concepts of both gravitational physics and differential geometry itself. In sprit, it is similar to celebrated texts such as Gravitation by Misner, Thorne, and Wheeler and Carroll's Spacetime and Geometry, in that it prioritizes physical intuition over rigorous formalism. Readers will find a comprehensive treatment of relativity, spanning from special to general relativity, with coverage of: Special relativity in differential geometric language — including uniformly accelerated motion, dynamics of massive and massless particles in flat spacetime, tensor analysis, and perfect fluids. Newtonian gravity and its incompatibility with special relativity, equivalence principles, gravitational redshift, relativistic effects in GPS, and the need for curved spacetime. Fundamentals of Riemannian geometry: manifolds, tensor fields, metric fields, Riemann normal coordinates, Levi-Civita tensors, exterior calculus, connections, geodesics, curvature, and Killing symmetries. Geodesic deviation, tidal forces, Einstein's field equations, weak-field approximation, and action principles. Schwarzschild spacetime, classical tests of general relativity, Schwarzschild black holes and their maximal extension, and gravitational collapse. Kerr spacetime, the Penrose process, black hole thermodynamics, and Hawking radiation. Basics of gravitational waves: origins, detection, and energy loss. The book also integrates modern developments, such as late-20th-century experimental tests, the effective field theory approach to general relativity, and modified theories of gravity. Suitable both as a textbook and a self-study reference, this work provides an accessible yet thorough journey into the geometric nature of gravity