Progress in the development of a theoretical subject is, to a great extent, predetermined by the adequacy, variety and power of the mathematical models used. Various mathematical tools have been utilised in circuit theory. They differ from one another in their complexity, generality and area of application. Thus, the topological properties of both linear and nonlinear electric circuits are best described by graph theory. Steady-state analysis of large linear circuits is carried out in the most effective way by using sparse matrix techniques. Qualitative properties of nonlinear circuits - existence,
uniqueness, boundedness of steady-states and other related topics - seem to be most adequately analyzed in terms of the qualitative theory of nonlinear differential equations.