TITLE: Where can I learn about Formal Schemes?
QUESTION [18 upvotes]: I am trying to learn formal schemes. I tried to read the section in Hartshorne but I don't get very far from there since things are not done quite explicitly enough, at least in my opinion.  I cannot read French, so EGA is out of the question.  I would really appreciate it if you could tell me a good introduction to this topic.

REPLY [4 votes]: If you are interested in the infinitesimal structure of formal schemes (with emphasis on non necessarily adic maps) I suggest to look at my papers with Jeremías and Pérez "Infinitesimal Lifting and Jacobi Criterion for Smoothness on Formal Schemes" (Comm. Alg.) and "Local structure theorems for smooth maps of formal schemes" (JPAA). Also for the deformation theory of formal schemes look at M. Pérez "Basic deformation theory of smooth formal schemes" J. Pure Appl. Algebra 212 (2008), pp. 2381–2388 (MR 2009h:14006). I apologize for this self-promotion...