These lecture notes provide a systematic introduction to matrix models of quantum field
theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix
formulation of non-commutative and fuzzy spaces followed by a description of the
non-perturbative treatment of the corresponding field theories. As an example the phase
structure of non-commutative phi-four theory is treated in great detail with a separate
chapter on the multitrace approach. The last chapter offers a general introduction to
non-commutative gauge theories while two appendices round out the text. Primarily written as a
self-study guide for postgraduate students - with the aim of pedagogically introducing them to
key analytical and numerical tools as well as useful physical models in applications - these
lecture notes will also benefit experienced researchers by providing a reference guide to the
fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy
geometries.
