Kosinski's "Differentiable Manifolds" and Milnor's h-cobordism theorem lecture notes I consider to be two of the standard high-dimensional manifold theory textbooks.
Kosinski, Differential Manifolds, Volume 138 (Pure and Applied Mathematics)
Milnor, John, Lectures on the h-cobordism theorem, notes by L. Siebenmann and J. Sondow, Princeton University Press, Princeton, NJ, 1965. v+116 pp.
another popular reference in the PL case is:
- Rourke, Colin Patrick; Sanderson, Brian Joseph, Introduction to piecewise-linear topology, Springer Study Edition, Springer-Verlag, Berlin-New York, 1982. ISBN 3-540-11102-6.
I believe they go as far as the $s$-cobordism theorem in that reference but I don't have a copy.
The standard references for the relationship between topological, smooth and PL structures would be Kirby and Siebenmann:
- Kirby, Robion C.; Siebenmann, Laurence C. (1977) Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. Princeton, NJ: Princeton Univ. Pr.. ISBN 0-691-08191-3
of all the above references I find this one the least reader-friendly, as it tends to be more heavy on technical constructions and steers-away from narrative. The above is still missing a lot of details -- for much of this material people still go back to Milnor's papers rather than book references. Milnor's writing is quite pleasant, for example you'll have to go there for his work on microbundles.