  This 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.
