In this book methods are proposed for solving certain problems in statistical physics which contain four-fermion interaction.It has been possible, by means of “approximating (trial) Hamil­ tonians”, to distinguish a whole class of exactly soluble model systems. An essential difference between the two types of problem with positive and negative four-fermion interaction is discovered and examined. The determination of exact solutions for the free energies, single-time and many-time correlation functions, T-products and Green’s functions is treated for each type of problem.The more general problem for which the Hamiltonian contains some terms with positive and others with negative four-fermion interaction is also investigated. On the basis of analysing and general­ izing the results of Chapters 1 to 3, it becomes possible to formulate and develop a new principle, the minimax principle, for problems in statistical physics (Chapter 4).