References for syntomic cohomology
I like the notes here, though I must confess I haven't read them completely. It has a nice introduction and explains the context.
I collected my very superficial knowledge only from browsing some articles, so that I can't give good bibl. hints. Perhaps some Besser's new construction of syntomic cohomology for smooth schemes or this article by Kato and Messing could be usefull.
Today new in the arxiv: "Cohomologie syntomique: liens avec les cohomologies étale et rigide".
Edit: Jan Nekovar announces an appendix to this article on "foundational aspects of syntomic topology and cohomology" (perhaps obtainable on request?) and mentions descriptions here and here.
Edit: It shows to be usefull to look (for the keywords in various languages) for exposé's of talks in the late 1980's explaining themes around Fontaine-Messing's article.