Abstarct: The purpose of this thesis is to classify invariant hypercomplex structures on a 4-dimensional real Lie group G. It is shown that the 4- dimensional simply connected Lie groups which admit invariant hypercomplex structures are the additive group H of the quaternions, the multiplicative group H* of nonzero quaternions, the solvable Lie groups acting simply transitively on the real and complex hyperbolic spaces, RH^4 and CH^2, respectively, and the semidirect product C⋊C. We show that the spaces CH^2 and C⋊C possess an RP^2 of (inequivalent) invariant hypercomplex structures while the remaining groups have only one, up to equivalence. Finally, thec corresponding hyperhermitian 4-manifolds are determined