TITLE: Advanced algebraic topology topics overview
QUESTION [23 upvotes]: Recently I became very much intrigued by algebraic topology and am spending quite some time learning it. My reasons are three-fold: 

it's a beautiful theory;
it gives geometric justification to (or perhaps rather an application of) many purely algebraic structures; and 
it has fascinating applications in quantum field theory and condensed matter theory.

Nevertheless, what I am familiar with currently are just basics: various homology and cohomology theories, homotopy theory and some standard applications (Brouwer, Borsuk-Ulam, etc., etc.). While these are of course interesting of and by themselves (and I expect spending a great amount of time on understanding all of this properly), I guess it is more or less understood for some fifty years now, so supposedly people work on topics far more advanced than this (or at the very least they use far more advanced tools to understand standard but hard problems).
So, I'd also like to know what the field is about from the modern perspective (some interesting problems and research topics, advanced tools, etc.) so that I can see a little where will the study of the subject lead me in the long run.
Sorry if the question is too broad but I am not sure where else to look (I've more or less browsed through all general articles on AT at wikipedia and tried to search MO too). I've heard few magic words like K-theory, sheaf cohomology, various spectral sequences, etc. but I don't understand these at all yet; more importantly my motivation to learn these things is lacking since I have no idea how or when these magic words are used (although I am pretty sure they are used a lot).

REPLY [7 votes]: The book which seems to me would best suit your needs is Switzer's Algebraic Topology- Homology and Homotopy, which gives very nice motivation, and leads right up to the 1970's state of the art (cobordisms, Steenrod algebra,...)
Then, the next book I would look at would recommend would be Rudyak's On Thom Spectra, Orientability, and Cobordism. Despite its fearsome title, this book seems to me like a really good volume 2 to Switzer, explaining clearly basic things like the relationship between homology and cobordism in low dimensions, which one doesn't find in other textbooks. Because TQFT is a functor from a bordism category, and especially in light of ETQFT work such as Hopkins-Lurie which is heavily algebraic-topological, my opinion is that these two books provide a bee-line the front lines of what you might in the future be interested in.