Stage 4

Equivalent to the (fourth) honours year in Australia, or the basic graduated year in other places. I shall outline the key topics and give short lists of references, you may scout around to see what makes you interest. I'm far from being an expert, let me know if you have a suggestion! Note that at this stage, the levels or difficulties of books within a certain topic may vary a lot. A few subfields may be highly related, e.g. further reading in Number Theory and algebraic geometry in Geometry. Moreover, further reading should belong to stage 5.