An exposition of part of an important subject which goes under the general name of inverse problems . The analogous problem for continuous media has been very much studied, with a great deal of difficult mathematics involved, especially partial differential equations. Some of the researchers working on the inverse conductivity problem for continuous media (the problem of recovering the conductivity inside from measurements on the outside) have taken an interest in the authors’ analysis of this similar problem for resistor networks. The authors’ treatment of inverse problems for electrical networks is at a fairly elementary level. It should be accessible to advanced undergraduates, and mathematics students at the graduate level. The topics should be of interest to mathematicians working on inverse problems, and possibly to electrical engineers. A few techniques from other areas of mathematics have been brought together in the treatment.