This is Part I of a two-part report on design and manufacturing methods used at SLAC to produce accelerator klystrons. Chapter 1 begins with the history and applications for klystrons, in both of which Stanford University was extensively involved. The remaining chapters review the theory of klystron operation, derive the principal formulae used in their design, and discuss the assumptions that they involve. These formulae are subsequently used in small-signal calculations of the frequency response of a particular klystron, whose performance is also simulated by two different computer codes. The results of calculations and simulations are compared to the actual performance of the klystron.