General relativity describes gravity as spacetime curvature rather than a force in the Newtonian sense. Matter and energy tell spacetime how to curve, and curved spacetime tells matter how to move. The central equation is Einstein's field equation, which relates geometry to stress-energy.

Effective field theory organizes physics by energy scale. Instead of demanding a single fundamental description at all scales, one writes the most general theory consistent with symmetry and includes higher-order corrections suppressed by a high-energy scale. This is a powerful way to make accurate predictions without full microscopic knowledge.

Many coupling constants depend on the energy scale at which a system is probed. Renormalization group ideas explain how physical behavior changes from short to long distances and why some theories are predictive over wide ranges of scale.

Current research includes quantum gravity, black hole thermodynamics, topological phases of matter, higher-dimensional field theories, and holographic duality. These topics use the same core ideas studied throughout the course: symmetry, action principles, fields, and approximation methods.