The first seven chapters of these notes reproduce the greatest part of a seminar held by the first author at
Princeton University during the spring semester, 1974. The
seminar was meant to provide the auditors with the basic
tools used in the study of crystalline cohomology of
algebraic varieties in positive characteristic, and did
not cover all known results on this topic. These notes
have the same limited purpose, and should really be"con-
be"considered only as an introduction to the subject.