The textbook aims to present general relativity and modern cosmology in a friendly form suitable for advanced undergraduates. The text begins with a self-contained introduction to the theory of manifolds and then develops the tools needed to understand curved spaces and curved spacetimes. Special relativity can then be understood in a geometrical context, bypassing some of the difficulties students have when encountering relativistic effects (e.g. time dilation and length contraction) for the first time. The theory of curvature and its effects leads to the Einstein field equations and its classic tests in the precession of Mercury and the deflection of starlight.The second part of the book covers modern cosmology, starting with the evolution equations for the expansion of the universe. The microwave background, evidence for dark matter, and the clustering of galaxies are examined in detail.