In Quelques proprietes globales des varietes differentiables, Thom classifies unoriented manifolds up to cobordism. I've been struggling a bit to understand this paper, and while Stong's cobordism notes have helped a bit, I was wondering if an English translation (of the entire paper or just parts) exists. Thank you in advance.
An English translation of this paper is included in the first volume of the "Topological Library", edited by Novikov and Taimanov. See the following website : http://www.worldscibooks.com/mathematics/6379.html
By the way, Thom's paper is rather hard to read. There are alternative expositions (often with somewhat easier proofs) of various pieces of it in various places. What portion in particular is giving you trouble?