Supersymmetric field theories of scalars and fermions in 4D space-time can be cast in the formalism of Kaehler geometry. In these lectures I review Kaehler geometry and its application to the construction and analysis of supersymmetric models on Kaehler coset manifolds. It is shown that anomalies can be eliminated by the introduction of line-bundle representations of the coset symmetry groups. Such anomaly-free models can be gauged consistently and used to construct alternatives to the usual MSSM and supersymmetric GUTs.

PACS numbers: 11.30.Pb, 12.60.Jv