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The paper develops a strictly mathematical unified theory of combinational switching networks of various types, with the aid of linear graph theory and lattice algebra. The switching net serves as the basic concept; it is defined as a directed, linear graph, the branches of which are weighted by elements of a distributive lattice. Similarly to the application of Boolean matrix theory to the study of relay-contact networks, the theory of switching nets makes use of a more general lattice matrix calculus. The paper includes, besides some new results, suitably modified, purely mathematical versions of known theorems on electrical contact networks.