Traditionally, \(p\)adic \(L\)functions have been constructed from complex \(L\)functions via special values and Iwasawa theory. In this volume, PerrinRiou presents a theory of \(p\)adic \(L\)functions coming directly from \(p\)adic Galois representations (or, more generally, from motives). This theory encompasses, in particular, a construction of the module of \(p\)adic \(L\)functions via the arithmetic theory and a conjectural definition of the \(p\)adic \(L\)function via its special values. Since the original publication of this book in French (see Astérisque 229, 1995), the field has undergone significant progress. These advances are noted in this English edition. Also, some minor improvements have been made to the text. Titles in this series are copublished with Société Mathématique de France. SMF members are entitled to AMS member discounts. Readership Graduate students and research mathematicians interested in number theory. Reviews "Written in a concise but readable style and can be recommended to readers interested in this rapidly growing subject."  European Mathematical Society Newsletter Table of Contents  Construction of the module of \(p\)adic \(L\)functions without factors at infinity
 Modules of \(p\)adic \(L\)functions of \(V\)
 Values of the module of \(p\)adic \(L\)functions
 The \(p\)adic \(L\)function of a motive
 Results in Galois cohomology
 The weak Leopoldt conjecture
 Local Tamagawa numbers and EulerPoincaré characteristic. Application to the functional equation
 Bibliography
 Index
