I am just about to finish my study of Milnor's book 'Topology from the Differentiable Viewpoint' and I really love the subject. I would like to continue my study of Differential Topology and am looking for some good references. What are the canonical choices of textbooks for this subject ? I am aware of the book by Morris Hirsch but am not sure what are the prerequisites or whether it is a good book. I have almost no knowledge of Algebraic Topology and my knowledge of analysis in limited to undergrad level real and functional analysis. I have a background knowledge of smooth manifolds and differential geometry (Riemannian metrics, curvature, connections etc.) Thanks !
If you're going to continue in topology, you should learn algebraic topology. Hatcher is a good place to start, and with your background, I would suggest Bott-Tu to bridge the gap between differential and algebraic topoogy.
For other differential topology books, Hirsch is good, as is Guillemin-Pollack. (The latter is standard introductory material; as I have not read Milnor's book, I do not know how strong the overlap is.)