In this chapter, we shall complete the classical (i.e., pre-gauge theory) analysis of the C ∞-topology of elliptic surfaces. In particular we shall compare deformation equivalence and diffeomorphism in all cases except when the fundamental group of the elliptic surface is finite cyclic. We shall also prove auxiliary results on the monodromy of general elliptic surfaces over ℙ1 and on the existence of embedded 2-spheres of self-intersection −2 in such surfaces.