This course presents an introduction to the principles and applications of detection and estimation theories. The main thrust is to show how statistical models can be used to provide optimal and suboptimal signal processing structures for digital communication systems operating over noisy channels. Topics covered include: classical detection theory and hypothesis testing, parameter estimation, binary and M-ary digital modulation, detection in coloured noise, coherent and non-coherent structures, detection of random signals in random noise, EM algorithm.