I am looking to learn about Riemann Surfaces but I know that beforehand I need to study certain subjects like Metric and Topological Spaces, Complex/Real Analysis and Complex Functions.
Can anyone give me some sort of subject tree that unites theses subjects and their pre-requisites, eventually leading to Riemann Surfaces?
I am a theoretical physics student so my background in mathematics is slightly different than that of the usual mathematics student. I have purchased a couple of books but I feel like I need a bit more structure and beginner's material to truly understand this branch of mathematics.
For studying Topology apart from familiarity with proof writing, some knowledge of Real Analysis is beneficial as it helps in understanding the motivation behind most of the concepts Moreover, most of the standard texts on Topology assume familiarity with Real Analysis, so it is better to know it beforehand.
Similar remarks hold for Complex analysis. To have a better motivation for studying Riemann Surfaces, it is good to know Complex Analysis and some Topology.