Prerequisites for Rigid Geometry I'm very interested in learning modern Rigid Geometry, but I'm not sure about the prerequisites for learning it.
I am a 3rd undergrad student majoring in Algebra and Topology. According to you, what is the ideal background I should have before diving into Rigid Geometry? What are some great resources (books, videos,..) about this topic that you would prefer to me?
Thanks
A bit about my current knowledge: Commutative Algebra up to Michale Atiyah, Algebraic Topology up to Hatcher, Fields and Galois theory up to Steven Roman, Manifolds (I haven't learned anything about smooth manifolds, I just finished Topological Manifold by John Lee), a bit about Homological Algebra and nothing about Algebraic Geometry.
 A: With your comment in mind, working towards perfectoid spaces, I can make a few suggestions.
The best source I can suggest are the Berkley lecture notes Lecture 1-7, maybe also 8-10 to actually see some strong tools around this theory.
Now while there is nothing stopping you from jumping right into these notes and trying to digest the material, I would add a small caveat.
Just as you can immediately start learning about algebra (field extensions, Galois theory...) without learning linear algebra before, you can also learn about rigid geometry without prior knowledge of algebraic geometry.
The problem that you might be facing is that often things might seem unmotivated, lacking intuition and difficult to understand. Things like sheaf theory are important, if not concretely, then at the very least on a conceptual level. These ideas came to life initially in algebraic geometry, when people introduced schemes, étale morphisms/topology etc. To a certain degree rigid geometry (whatever that is supposed to mean) was developed after algebraic geometry, in parts it aims to mimic it.
Thus let me suggest that it is very helpful to first learn about algebraic geometry (along the lines of Hartshorne Chapter II or Götz and Wedhorn's Algebraic geometry and other possible sources) and also something about non-archimedean fields/algebraic number theory (along the lines of Serre's Local fields). Certainly there is no need to learn everything up to the last detail, but working with these objects will give you an indispensible intuition.
Afterwards you can think, if you first want to read about rigid-analytic spaces à la Tate (Bosch's Lectures on Formal and Rigid Geometry is a great resource here) or jump right into action in the aforementioned source. I personally did the latter and didn't find it to be such a big hassle. A great supplement to the Berkeley notes are the notes from  this Number theory seminar. You can of course also read about perfectoid spaces straight from the source in the survey paper, but I found this to be more technical. In any case it is a great back-up source. Also you can find more references in these study group notes.
