This is a one semester text for students in mathematics, engineering, and statistics. Most of the work that has been done on Kalman filter was done outside of the mathematics and statistics communities, and in the spirit of true academic parochialism was, with a few notable exceptions, ignored by them. This text is Catlin's small effort toward closing that chasm. For mathematics students, the Kalman filtering theorem is a beautiful illustration of Functional Analysis in action; Hilbert spaces being used to solve an extremely important problem in applied mathematics. For statistics students, the Kalman filter is a vivid example of Bayesian statistics in action.