  These notes are intended as an introduction to noncommutative (quantum)
filtering theory. An introduction to quantum probability theory is given,
focusing on the spectral theorem and the conditional expectation as the least
squares estimate, and culminating in the construction of Wiener and Poisson
processes on the Fock space. Next we describe the Hudson-Parthasarathy quantum
Ito calculus and its use in the modelling of physical systems. Finally, we use
a reference probability method to obtain quantum filtering equations, in the
Belavkin-Zakai (unnormalized) form, for several system-observation models from
quantum optics. The normalized (Belavkin-Kushner-Stratonovich) form is obtained
through a noncommutative analogue of the Kallianpur-Striebel formula.
