I've recently started learning about topological insulators. I've read a considerable amount of (review) papers on the subject, yet I still only have a phenomenological understanding of what a topological insulator is. I know for example, that the gapless surface states have to be there because of the change from a topologically nontrivial to a topologically trivial state (for example the vacuum). However, I could only explain this in terms of a comparison to changing a trefoil knot to a torus. Also, I wouldn't know why the surface states are topologically protected and what time-reversal symmetry has to do with that. I have a background in quantum mechanics / solid state physics, ranging up to the start of 2nd quantization (in the sense that i know what a creation/annihilation operator is). So my question is: could anybody give me some pointers on where to start reading up on the topic? Where do I take it from here? Thanks.