This book is devoted to the study of various spaces of holomorphic functions on the unit ball. The main tool used for their study is an explicit form of the Bergman and Cauchy-Szëgo kernels. There is a lot of different spaces of that sort and the author has chosen some of them for a detailed study. There is always one chapter of the book devoted to one type of function spaces. The spaces treated in the book are Bergman spaces, Bloch space, Hardy spaces, spaces of functions with bounded mean oscillation (BMO), Besov spaces and Lipschitz spaces. The author discusses the various characterizations, atomic decompositions, interpolations, and duality properties of each type of function space in turn. To read the book, knowledge of standard complex function theory is expected but the theory of several complex variables is not a prerequisite. Results presented are standard but their proofs are often new.