Logarithmic differential forms

In the talk we discuss some aspects of the theory of logarithmic differential forms and their applictations. We begin with a historical review and elementary facts. Then we present author's results on logarithmic forms obtained in terms of the de Rham complex on hypersurfaces with arbitrary singularities. We pay attention to the relation with a classical residue theory of Cauchy and Poincaré, with a torsion theory of regular differentials, with a theory of regular meromorphic differential forms.