This book is the first of its kind in world literature—a textbook-monograph on the theory of unconventional superconductivity (superconductivity with non-trivial Cooper pairing). The book is divided into two parts. The first part presents a symmetry classification of superconducting phases, the Bardeen-Cooper-Schrieffer theory, and the Ginzburg-Landau-Abrikosov theory, along with a description of several effects specific to unconventional superconductors. It employs general concepts from quantum mechanics and statistical physics (including the method of second quantization), making the material accessible to a broad audience of experimental and theoretical physicists across various specialties, as well as physics students. The second part includes a series of problems related to the theory of unconventional superconductivity, the solutions to which require the application of Green's function techniques (Gorkov's equations). Reading this section assumes that the readers have the appropriate background and will primarily benefit theoretical physicists, graduate students, and undergraduates specializing in theoretical physics. The book features several original results from the authors, adding to its unique contribution to the field.