In 2004, I was asked by Professor King Fai Lai to come to Peking University in order to give a course on rigid cohomology. We agreed on the last two weeks of January 2005. I want to thank here Professor Zhao Chunlai for the organization of my visit as well as Professor Zhou Jian and his wife for showing us the city. My family and I will always remember it.

While preparing this course, I realized that there was no introductory book on rigid cohomology. Actually, there was no available material in English and only an old document in French, Cohomologie rigide et cohomologie rigide à support propre, by Pierre Berthelot. A revised version of the first part of this document appeared as an official preprint in 1996 but the second part is not fully written yet and, therefore, not really available to the mathematical community. Fortunately, Berthelot was kind enough to answer my questions on this second part and point out some articles where I could find some more information.

Rigid cohomology was introduced by Berthelot as a p-adic analogue of l-adic cohomology for lisse sheaves, generalizing Monsky—Washnitzer theory as well as crystalline cohomology (up to torsion). Recently, it appeared that this theory may be used in order to derive new algorithms for cryptography.