While systems at equilibrium are treated in a unified manner through the partition function formalism, the statistical physics of out-of-equilibrium systems covers a large variety of situations that are often without apparent connection. This book proposes a unified perspective on the whole set of systems near equilibrium: it brings out the profound unity of the laws which govern them and gathers a large number of results usually fragmented in the literature. The reader will find in this book a pedagogical account of the fundamental results: physical origins of irreversibility, fluctuation-dissipation theorem, Boltzmann equation, linear response, Onsager relations, transport phenomena, Langevin and Fokker-Planck equations. The book's comprehensive organisation makes it valuable both as a textbook about irreversible phenomena and as a reference book for researchers.