The operational deployment of WSR–88D radars throughout the USA can be considered as a major milestone in the application of the Doppler principle to radar meteorology. Throughout the world, the operational use of Doppler radars is considered to be an indispensable tool for monitoring the development of hazardous storms. Doppler radar theory and techniques in meteorology have reached a level of maturity where even the non-specialist can begin to use and apply the data with little formal training. This chapter attempts to provide the interested reader with a fairly rigorous approach to Doppler radar principles. Following a very brief review of signal and system theory, the received voltage from a random distribution of precipitation particles is formulated for an arbitrary transmitted waveform. The expression for mean power is formulated in terms of the intrinsic reflectivity and a three-dimensional weighting function. The range–time autocorrelation function of the received voltage is formulated in terms of the range–time profile of the time-correlated scattering cross section of the particles and of the time correlation of the transmitted waveform. Next, the sample–time autocorrelation function is derived and the concept of coherency time of the precipitation medium is introduced, which dictates the pulse repetition time for coherent phase measurement. The concept of a spaced-time–spaced-frequency coherency function is introduced, to illustrate how frequency diversity can be used to obtain nearly uncorrelated voltage samples from the same resolution volume.