In Chapter 1, some of the topics in the conventional circuit theory are reviewed, which have particular importance in the theory of microwave circuits. There include the theory of transmission line, bilinear transformations, and power waves. Chapter 2 gives a review of vector analysis and the fundamental properties of electromagnetic fields to facilitate our later study. In Chapter 3, waveguides are discussed for the first time. Here, the eigenvalue problem is studies in detail including the completeness of eigenfunctions. Without the discussion of the completeness, the theory is only partially correct since no answer is given to certain fundamental questions such as why an exponential variation with distance is assumed for each mode and no other possible functional form is considerer. Chapter 4 discusses resonant cavities using a similar eigenfunction approach. In Chapter 5, various properties of waveguide junctions are discusses using matrices. Matrices are introduced since the multitude of symbols and lengthy expressions, which would otherwise be necessary,, could interfere wirh our concentration on the heart of a problem. Just as vectors do, matrices help in studying relatively complex problems, systematically. Chapter 6 discusses two phenomena: electromagnetic fields in cavities. Each illustrates an interesing application of eigenvalue problems. Chapter 7 is a study of linear amplifiers. The central topic is their noise performance. In Chapter 8, we discuss a circuit-theoretical analysis of electron beams which clarifies a number of properties of practical interest. Finally, Chapter 9 contains a discussion of oscillators. Although osciallators are inherently nonlinear, some of their important properties are studies here without specifying the details of the nonlinearity.