Non Archimedean L Functions and Arithmetical Siegel Modular Forms : Second Augmented Edition This book is devoted to the arithmetical theory of Siegel modular forms and their L functions. The central object are L functions of classical Siegel modular forms whose special values are studied using the Rankin Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p adic interpolation of these critical values is presented. An important class of p adic L functions treated in the present book are p adic L functions of Siegel modular forms having logarithmic growth (which were first introduced by Amice Velu and Vishik in the elliptic modular case when they come from a good supersingular reduction of ellptic curves and abelian varieties). The given construction of these p adic L functions uses precise algebraic properties of the arihmetical Shimura differential operator. The book could be very useful for postgraduate students and for non experts giving a quick access to a rapidly developping domain of algebraic number theory: the arithmetical theory of L functions and modular forms