This bachelor's degree thesis is an introduction to the Theory of General Relativity (GR), a relativistic theory of gravity, from the point of view of a recently graduated mathematitian. The principles of GR are stated and some motivation on the formulation of the theory is provided. It is shown that freely-falling particles move along geodesics of spacetime and Einstein's equations are derived as a generalization of Newton's gravity. The uniqueness of Einstein's equations and the presence of the cosmological constant are discussed. The thesis concludes finding Schwarzschild solution by assuming that there exists a spherically symmetric metric that is a solution to Einstein's equations in vacuum and seeing what properties should this metric have. The boundary conditions imposed are the existence of a punctual uncharged mass at the origin and flatness of the metric at infinity. The result is a particular solution that can be applied in many contexts, such as in the Solar System.

Se trata de hacer una presentación de los fundamentos, ecuaciones y algunos aspectos fenomenológicos de la Teoría General de la Relatividad, desde un punto de vista matemático formal. En particular:- Repasar algunos conceptos básicos de geometría diferencial.- Analizar los antecedentes y los postulados de la Relatividad General.- Obtener las ecuaciones de Einstein y estudiar su formulación variacional (lagrangiana de Hilbert).- Describir algunas consecuencias fenomenológicas y cosmológicas de la teoría.