The monograph was written by the largest American theoretical physicist E. Wigner and a well-known expert in reactor theory A. Weinberg and is devoted to the consideration of the physical processes underlying the operation of reactors of all important types. The theory of homogeneous and heterogeneous reactors on thermal, resonant and fast neutrons is described in detail, the equations describing the distribution of neutron flux in the reactor are analyzed in detail, the statics and dynamics of the reactor are studied. Particular attention is paid to a deep physical interpretation of the issues under consideration, comparison of the results of calculations with the experiment. This monograph is intended for physicists and engineers engaged in the calculation and design of reactors. It will also be useful for students and graduate students preparing for work in the field of reactors, to deepen their knowledge in their chosen specialty.