These two volumes collect together lectures given at the intensive “Dwork Trimester in Italy”, which was held from May to July 2001 at the University of Padova. As these facts indicate, the focus of the papers collected in the proceedings is on the many p-adic facets of Dwork’s contributions to mathematics. The collection of papers comprises more than a thousand pages, the papers being written by leading experts in the field. The reader will find here not only overview and introductory papers but also research articles on some very attractive applications of p-adic techniques in algebraic geometry, the theory of modular form, differential or difference equations and in homology algebra. The range of topics covered by the papers is wide, including variations of p-adic cohomology of families of exponential sums, p-adic analogues of hypergeometric functions, the Dwork trace formula, the celebrated Grothendieck’s conjecture on differential linear equations and N. Katz’s reformulation. The proceedings will be useful for a wide range of readers interested in modern applications of p-adic methods.