Switching fabrics first appeared in telephone exchanges, where there was a need to interconnect many pairs of telephones installed in the network. Due to the large number of connected subscribers and int- exchange links, switching fabrics in telephone exchanges have to serve a great number of input and output ports. Because of the scale, large switching fabrics were constructed from smaller ones. The way of building switching fabrics from elements of smaller capacity and different characteristics of switching fabrics topologies has been for a long time a rich area of theoretical research. The seminal work is due to C. Clos [23], who first considered multistage strict-sense nonblocking switching networks, and V. E. Benes [9], who first introduced the mathemati cal theory of switching networks. From that time, many research was conducted in this field. Switching fabrics found its application not only in telecommunication, starting from telephone exchanges through ATM switches and IP routers to optical cross-connect systems and optical packet switches, but also in other areas of knowledge like computation and control. Theory of switching fabrics becomes also a part of applied mathematics. Results of studies carried out by researchers from these area were published in numerous papers and some books. This book is intended for people interested in the switching the ory, and especially combinatorial characteristics of switching networks. It contains a considerable amount of already known results. Some of them are presented in more detailed form, other are only mentioned.