This high-level undergraduate text explains the mathematics behind basic circuit theory. Its self-contained treatment covers matrix algebra, which provides a general means of formulating the details of a linear system. In addition, the author presents the basic theory of n-dimensional spaces and demonstrates its application to linear systems. A development of the mathematics of matrix algebra and determinants is followed by the application of matrix techniques to a general discussion of circuits. Subsequent topics include the properties of active and passive two-port devices, the basic theory of linear vector spaces, and the natural frequencies of a network. Appendixes cover the indefinite-transfer matrix, gyrators with complex gyration admittance, and network transformations. A wealth of equations and calculation problems appear throughout the text.