This is the first course of a two-term sequence on stochastic systems designed to cover some of the basic results on estimation, identification, stochastic control and adaptive control. Topics include: stochastic processes and their descriptions, analysis of linear systems with random inputs; prediction and filtering theory: prediction for ARMAX systems, the Kalman filter and the Riccati equation; stochastic control methods based on dynamic programming; the LQG problem and the separation theorem; minimum variance control.