As I'm constantly running across higher categories these days, I'm wondering what is a good starting point to get into the theory?
While I am aware of nLab and the n-Category Café, I am having a real hard time getting into the material provided. One reason for this is: afaik there is no generally favored way of defining higher categories, and different approaches lead to different properties / results / theories. This naturally leads to lots and lots of texts concerned with fundamental questions, such as comparison of these different approaches, which I am not interested in too much.
Lets be a little more precise with what I'm actually looking for: A straight forward introduction to one theory of weak higher categories, with applications in algebraic topology.
I hope someone here has already went through this search and is willing to post a guideline or at least some recommendations.
After a complete day of searching the web, I have finally found something very promising although it seems to only deal with strict $\omega$-groupoids: The still to be published book Nonabelian Algebraic Topology by Ronald Brown, Philip J. Higgins and Rafael Sivera. A draft is downloadable on this website too.