It is well known that there is a correspondence between homomorphism of rings $A\to B$ and morphism of affine schemes $\mathrm{Spec}(B) \to \mathrm{Spec}(A)$.


**Question:** (1) In analogy, is there anything similar between homomorphism of adic rings and morphisms of affine formal schemes $\mathrm{Spf}(B)\to \mathrm{Spf}(A)$? 
(2)What could be good references for this?



about morphisms of affine formal schemes $\mathrm{Spf}(B)\to \mathrm{Spf}(A)$
See EGA I, sec. 10. For the specific question you mention, see paragraph 10.2. There is further issues on the cohomology of formal schemes in EGA III, sect 3.4. Also, the existence theorem is treated in the volume "Fundamental Algebraic Geometry: Grothendieck’s FGA explained", Mathematical Surveys and Monographs 123 (2006), A.M.S.


