I really enjoy doing maths and it fills quite a lot of my spare time. I'm starting my first year in the university on october and I probably won't have that much time for independent reading once there.
I have been reading maths (on and off) for years now and have the necessary background in topology, analysis (although i would say my grip on analysis ins't the best - i.e. I wouldn't be able to really enjoy a serious book on functional analysis) and algebra to read in one of two categories that interest me:
(1) Differential Topology\Manifolds - (co-)tangent space, fibre bundles, vector fields... etc.
(2) Algebraic Topology - (co-)homology, homotopy, covering spaces... etc.
My question is what of the two would I be more likely to encounter in my future studies?
In other words: what will be more valuable for me to study independently while i still have the time?
I already have books I like but am unsure about what topic to pick.