2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104631This is a preliminary version, comments and inputs are welcome. Contents: 1. Introduction. 2. Fuzzy Spaces. 3. Star Products. 4. Scalar Fields on the Fuzzy Sphere. 5. Instantons, Monopoles and Projective Modules. 6. Fuzzy Nonlinear Sigma Models. 7. Fuzzy Gauge Theories. 8. The Dirac Operator and Axial Anomaly. 9. Fuzzy Supersymmetry. 10.Fuzzy Spaces as Hopf Algebras.136 pages, LaTeX, A substantially revised and updated version is being published by World ScientificHigh Energy Physics - TheoryGeneral Relativity and Quantum CosmologyHigh Energy Physics - LatticeHigh Energy Physics - PhenomenologyMathematical PhysicsQuantum AlgebraQuantum Physicstext