I am looking for a guidance in $K$-theory. My master thesis was in the field of Algebraic K-theory and its relation and interaction with the field of Algebraic Topology. I mainly had concentrated on the study of the third K-group of an infinite field. I studied the Anderie Suslin paper, which was titled as the "$K_3$ of a field, and the Bloch group". Entering to this field required my hard work on algebraic topology. By now I am a Ph.D. student, and I do not have my master supervisor here. I always see $K$-theory as a giant which has many things in his heart. I am much interested in it, but I do not how should I walk into this realm. I may have a question from the experts: I know some preliminaries, and I want to fulfill my dreams about $K$-theory, what is the main plan? What kind of requirements I need?

I have studied several books in this branch, Hatcher for first, Sirinivas, Atiyah, and many lectures and some papers. I have good background in Homology and Algebraic geometry too.

Your comments and suggestions would be greatly appreciated.

On the cohomology and K-theory of the general linear group over a finite field. I was just trying to limit the list to a manageable starting point in my answer, there are so many great papers in the subject... $\endgroup$ – Denis Nardin Jun 3 '18 at 6:35