Hi everyone,


I'm looking for a systematical introduction to (or treatment of) logarithmic structures on schemes. I am reading Kato's article ("Logarithmic structures of Fontaine-Illusie") at the moment, but I would like to have a more detailed source that goes through or gives an overview of the constructions of classical scheme theory that have analogs in the log-setup.
Are there any articles/books that in your opinion are required reading if I want to learn about log-geometry? What are beautiful examples of applications of this machinery?



References for logarithmic geometry
I put up some old notes by Illusie [here](http://math.harvard.edu/~tdp/Illusie-Log.geometry.lecture.notes-single-page.pdf) for you; they're very detailed and treat log smoothness, the log de Rham complex, and other topics in their second exposé. They're my favourite first reference.


There is also Ogus's book, the latest draft of which is [here](http://math.berkeley.edu/~ogus/preprints/log_book/logbook.pdf).


