Lectures on matrix field theory / Badis Ydri.

Includes bibliographical references and index.

1. Introductory Remarks.-
2. The Non-Commutative Moyal-Weyl Spaces Rd.-
3. The Fuzzy Sphere.-
4. Quantum Non-Commutative Phi-Four.-
5. The Multitrace Approach.-
6. Non-Commutative Gauge Theory.

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.