  The present article contains a short introduction to Modular Theory for von
Neumann algebras with a cyclic and separating vector. It includes the
formulation of the central result in this area, the Tomita-Takesaki theorem,
and several of its consequences. We illustrate this theory through several
elementary examples. We also present more elaborate examples and compute
modular objects for a discrete crossed product and for the algebra of canonical
anticommutation relations (CAR-algebra) in a Fock representation.
