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