The primary purpose of these notes is to sketch an approach to the elementary algebraic theory of planar electric networks which conduces to a formal dual correspondence between the so-called mesh and nodal representations of planar networks that is complete in every respects It is also shown that if general variables are employed in the analysis of a network the number of voltage or current equations that serve to describe the network is infinite. Finally, it is demonstrated that the impedance or admittance matrix of a passive network is not necessarily symmetrical.