Estimation theory is a branch of statistics and signal processing dealing with the estimation of the values of parameters based on a measured data set. This chapter describes the main components of a system, namely, the transmitter, channel, and receiver. It introduces the basics of communication theory and deals with signal transmission through channels, distortionless transmission, bandwidth of the signal, relation between bandwidth and rise time, the Paley–Wiener theorem, ideal low-pass filters, high-pass filters, bandpass filters, and so on. The chapter discusses optimum detection methods. These methods include weighted probability tests, maximum likelihood criterion, Bayes criteria, minimax criteria, Neyman–Pearson criteria, and receiver operating characteristics. The aim of any communication, control, or radar system is to design a receiver that will maximize the information of the detected signal. The theory of optimum receivers is based on the concepts of information theory and detection theory. The receivers are designed to maximize signal-to-noise ratio or minimize the error rate.