The goal of this talk is threefold. First, we define a common
generalization of the classical torsion over commutative domains and 
the 1-torsion (i.e., the kernel of the map from a module to its bidual) 
of finitely presented modules over arbitrary rings. This is done without 
any assumption on the ring or the module. Secondly, based on this 
definition, we introduce (again in full generality) a dual concept of the 
cotorsion module of a module. Unlike torsion, this concept does not 
seem to have a classical prototype. Thirdly, we describe various dualities 
between the two concepts.