It looks like there is some literature out there on what might be called 'non-Archimedean complex analysis' e.g. Benedetto - An Ahlfors Islands Theorem for non-archimedean meromorphic functions and Cherry - Lectures on Non-Archimedean Function Theory. I am mainly working on non-Archimedean functional analysis right now and need to become better acquainted with the non-Archimedean analogues of basic results that might be encountered in a first course on complex analysis, up to and including Liouville's Theorem e.g. Cauchy integral formulas, holomorphic functions etc. for a few spectral theory proofs.
Of course I am well aware that with many results there will be no such analogue. What I would like to know is if there exists a good introduction to this area that I could look at, that starts with the fundamentals. For example, is there an analogue of 'holomorphic iff analytic'? Any advice much appreciated.
This relates to my earlier question: Non-emptiness of spectrum σ(a) in non-Archimedean Banach algebras