“The book is thorough and very carefully written, with useful appendices on classical rigid cohomology, adic spaces and cohomological descent. Moreover, instead of deducing results from the known cases in classical rigid cohomology (when possible), the authors have the choice of writing down complete proofs in their setting. This makes the exposition clearer and the book self-contained. I believe that it will soon become a reference on the subject … .” (Jérôme Poineau, zbMATH 1400.14002, 2019)

• Introduction.- First definitions and basic properties.- Finiteness with coefficients via a local monodromy theorem.- The overconvergent site, descent, and cohomology with compact support.- Absolute coefficients and arithmetic applications.- Rigid cohomology.- Adic spaces and rigid spaces.- Cohomological descent.- Index

“The book is thorough and very carefully written, with useful appendices on classical rigid cohomology, adic spaces and cohomological descent. Moreover, instead of deducing results from the known cases in classical rigid cohomology (when possible), the authors have the choice of writing down complete proofs in their setting. This makes the exposition clearer and the book self-contained. I believe that it will soon become a reference on the subject … .” (Jérôme Poineau, zbMATH 1400.14002, 2019)

• Introduction.- First definitions and basic properties.- Finiteness with coefficients via a local monodromy theorem.- The overconvergent site, descent, and cohomology with compact support.- Absolute coefficients and arithmetic applications.- Rigid cohomology.- Adic spaces and rigid spaces.- Cohomological descent.- Index

“The book is thorough and very carefully written, with useful appendices on classical rigid cohomology, adic spaces and cohomological descent. Moreover, instead of deducing results from the known cases in classical rigid cohomology (when possible), the authors have the choice of writing down complete proofs in their setting. This makes the exposition clearer and the book self-contained. I believe that it will soon become a reference on the subject … .” (Jérôme Poineau, zbMATH 1400.14002, 2019)

• Introduction.- First definitions and basic properties.- Finiteness with coefficients via a local monodromy theorem.- The overconvergent site, descent, and cohomology with compact support.- Absolute coefficients and arithmetic applications.- Rigid cohomology.- Adic spaces and rigid spaces.- Cohomological descent.- Index