Diffeomorphisms of Elliptic 3 Manifolds 1 Elliptic 3 manifolds and the Smale Conjecture 2 Diffeomorphisms and Embeddings of Manifolds 3 The Method of Cerf and Palais 4 Elliptic 3 manifolds Containing One sided Klein Bottles 5 Lens Spaces This work concerns the diffeomorphism groups of 3 manifolds in particular of elliptic 3 manifolds. These are the closed 3 manifolds that admit a Riemannian metric of constant positive curvature now known to be exactly the closed 3 manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3 manifold M the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture for the 3 sphere was proven by J. Cerf and A. Hatcher and N. Ivanov proved the generalized conjecture for many of the elliptic 3 manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3 manifolds containing geometrically incompressible Klein bottles and for all lens spaces L(m q) with m at least 3. Additional results imply that for a Haken Seifert fibered 3 manifold V the space of Seifert fiberings has contractible components and apart from a small list of known exceptions is contractible. Considerable foundational and background material on diffeomorphism groups is included