  Let X be a geometrically irreducible smooth projective curve over a field k.
We describe the algebra of endomorphisms of indecomposable unstable vector
bundles over X of rank 2 and degree d. Fixing some numerical invariants, namely
the Harder-Narasimhan type and the dimension of the algebra of endomorphisms,
we construct algebraic stacks and moduli schemes for such bundles.
