This introductory textbook describes modern cosmology at a level suitable for advanced undergraduates who are familiar with mathematical methods and basic theoretical physics. An introductory survey of the large scale structure of the universe is followed by an outline of general relativity. This is then used to construct the standard models of the universe. The very early and early stages of the Big Bang are described, and this includes primordial nucleosynthesis, grand unified theories, primordial black holes, and the era of quantum cosmology. The problem of the formation of structure in the universe is then addressed. This textbook concludes with brief outlines of alternative cosmologies. It includes 400 problems for students to solve, and is accompanied by numerous worked examples.