Currently I'm self studying for my own enjoyment topology and algebra (munkres and herstein). Since I start at the university next year everything I'm learning now is for my own enjoyment and I will probably relearn it in the university anyway.
I'm interested in differential topology yet I haven't read a single book on analysis in the level of say, "baby Rudin". Not to say that I'm not familiar with it. I have done a lot of studying in the past on calculus (sequences, differentiation, integration, fourier series, integral transforms etc.) ODE's (and a bit PDE's) and non rigorous complex analysis (visual complex analysis) but my foundation are really far from being solid.
Is it possible to learn differential topology before strengthening my foundations in analysis and leave that to do once i get to the university?