Free online courseGeneral Relativity of Einstein

Course Description

General Relativity can feel like a wall of equations until you see the simple idea behind it: gravity is not a mysterious force acting at a distance, but the geometry of spacetime itself. In this free online course, you build that geometric intuition step by step and learn how to translate it into the mathematical language physicists use to make real predictions.

The course begins by reframing physics through symmetry, invariants and spacetime viewpoints that unify motion and gravity. From there, you develop comfort with tensors, the natural tools for expressing physical laws in any coordinate system. Rather than treating tensors as abstract symbols, you learn why they matter: they keep your equations meaningful when you change perspective, and they reveal what is truly physical versus what is just a coordinate choice.

As the ideas deepen, you connect conservation laws to volume elements and curved geometry, then move into the objects that carry physical content in relativity, such as the stress-energy tensor, and the geometric quantities that encode how coordinates and vectors vary in curved spacetime. With the equivalence principle as a guiding theme, the course shows how free fall, inertial motion and gravitational effects become the same story told in the right language, leading naturally to concepts like parallel transport, symmetries in spacetime and geodesics.

You then reach the heart of the subject: curvature and the Einstein field equation, including insight into why the equation has the form it does and how matter tells spacetime how to curve. With that foundation, you explore approximations that make the theory usable in practical settings, including linearized gravity and the transition from static limits to dynamical sources. From there, the course opens the door to gravitational radiation, cosmology, compact spherical sources and the physics of black holes, tying mathematical structure to phenomena that shape modern astronomy and cosmology.

Exercises throughout help you check understanding and gain fluency, whether you are strengthening school physics knowledge, preparing for university-level studies, or revisiting relativity with clearer intuition. By the end, you will be able to read core formulas of General Relativity with confidence and understand what they say about the universe.