This textbook is designed both for serious students of physics and astrophysics and for those with a particular interest in learning about theoretical cosmology. There are already many books that survey current observations and describe theoretical results; my goal is to complement the existing literature and to show where the theoretical results come from. Cosmology uses methods from nearly all fields of theoretical physics, among which are General Relativity, thermodynamics and statistical physics, nuclear physics, atomic physics, kinetic theory, particle physics and field theory. I wanted to make the book useful for undergraduate students and, therefore, decided not to assume preliminary knowledge in any specialized field. With very few exceptions, the derivation of every formula in the book begins with basic physical principles from undergraduate courses. Every chapter starts with a general elementary introduction. For example, I have tried to make such a geometrical topic as conformal diagrams understandable even to those who have only a vague idea about General Relativity. The derivations of the renormalization group equation, the effective potential, the non-conservation of fermion number, and quantum cosmological perturbations should also, in principle, require no prior knowledge of quantum field theory. All elements of the Standard Model of particle physics needed in cosmological applications are derived from the initial idea of gauge invariance of the electromagnetic field. Of course, some knowledge of general relativity and particle physics would be helpful, but this is not a necessary condition for understanding the book.