We study some algebras generated by the singular integral operator with the quaternionic Cauchy kernel and the multiplication operators by continuous or piece-wise continuous functions. This allows us to describe the Fredholm theory of hyperholomorphic Riemann boundary value problems whose formulations take into account both the non-commutativity of the quaternionic multiplication and the existence of various classes of hyperholomorphic functions. Certain classes of hyperholomorphic Toenlitz operators are also studied.