Abstract: In order to describe linear representations of a group, it is sufficient to find all its indecomposable representations. It is known that indecomposable algebraic representations of G=SL(2) correspond to irreducible subrepresentations of G in the ring R of polynomials in two variables x and y. Given a derivation ' on the ground field, R extends to a G-representation R' by adding variables x', y', x", y", etc. We will investigate indecomposable subrepresentations of R' and discuss their relation to description of all differential representations of G. If time permits, I will describe the category of differential representations of tori.