Where should I learn about immersion theory? I'd like to learn the basics of Hirsch-Smale immersion theory.  What sources are best for this?  My background is mostly topological; however, many of the sources I've found on the internet focused on later work of Gromov on the h-principle which seems more analytic than I would like.
 A: M. Weiss has a very good survey on his homepage:
http://wwwmath.uni-muenster.de/u/mweis_02/papers.html
called "Immersion theory for homotopy theorists". I also like very much M. Adachi's book "Embeddings and immersions". I think both are very good starters if you have a topological background. 
J. Francis has also some notes on his homepage:
http://www.math.northwestern.edu/~jnkf/classes/hprin/
on a course about the h-principle that can be helpful. 
Also Eliashberg and Mischachev's book "introduction to the h-principle" is definitively a very good book.  
A: You may like the following lecture notes:
Weiss, M. Immersion theory for homotopy theorists
Francis, J. The h-principle in topology
A: Immersion theory has been "explained" by the Compression Theorem, with new proofs arguably being much more elementary and intuitive:
Rourke and Sanderson, 
A master's thesis with another exposition
A: I think this is the most readable source:
Haefliger, A.
Lectures on the theorem of Gromov. Proceedings of Liverpool Singularities Symposium, II (1969/1970), pp. 128–141. Lecture Notes in Math., Vol. 209, Springer, Berlin, 1971. 
