  The subject of matrix field theory involves matrix models, noncommutative
geometry, fuzzy physics and noncommutative field theory and their interplay. In
these lectures, a lot of emphasis is placed on the matrix formulation of
noncommutative and fuzzy spaces, and on the non-perturbative treatment of the
corresponding field theories. In particular, the phase structure of
noncommutative $\phi^4$ theory is treated in great detail, and an introduction
to noncommutative gauge theory is given.
