Abstract: We construct left invariant complex structures on affine Lie groups. As an application, we obtain a complex structure on (S¹)^kxE(n) for k=0 or 1, where S¹ denotes de circle and E(n) the Euclidean group and on the Poincare group P⁴ⁿ⁺³. For an arbitrary Lie group G, we study sufficient conditions which allow to define a natural complex and symplectic structure on its tangent bundle TG. If the Lie group G is equipped with a flat torsion free connection and a parallel complex structure, then TG carries a hypercomplex structure and, by an iterative procedure, we can obtain Lie groups with a family of complex structures generating any prescribed real Clifford algebra.