Physical Aspects of Differential Calculi on Commutative Algebras

The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of differential calculi on commutative algebras (which can be regarded as algebras of functions on some topological space). We explain how these are related to relevant structures in physics.