This course gives thorough knowledge of linear estimation theory. The main theme of the course is optimal linear estimation, Kalman and Wiener filtering, which are systematic methods to solve estimation problems with applications in several technical disciplines, for example in telecommunications, automatic control and signal processing but also in other disciplines, such as econometrics and statistics.The course also provides an introduction to optimal filtering for non-linear systems. The course assumes familiarity with basic concepts from matrix theory, stochastic processes, and linear systems theory. The course is directed towards the students who intend to work with development and research within these fields.