EE-562 has been designed mainly to provide a good understanding of fundamentals of Detection Theory and Estimation Theory. The former is used, for example, in digital communications to recover transmitted messages received in noise. The latter has application, e.g., in radar measurements or in tracking moving targets where certain random parameters need to be estimated, based on available noisy measurements. The course starts with an introduction to the optimal processing of communication signals. Then it visits the binary hypothesis-testing problem. This is followed by Bayes risk and Neyman-Pearson criteria based receivers and M-ary hypothesis detection problems along with Composite hypothesis problems. Parameter estimation criteria; Cramer-Rao bounds; maximum-likelihood estimation, Integral equations; the Karhunen-Loeve Expansion Theorem are then covered. Detection problems of signals in additive white Gaussian noise and Detection problems in colored noise, the whitening filter are covered next. Classical signal estimation problems: Multiple Channels and Multiple Parameter Estimation and Estimation of Continuous Waveforms are covered. The Linear Estimation-Wiener-Hopf Equations are covered. The Wiener and the Kalman-Bucy filters are covered. Sequential detection and non-parametric estimation are introduced.