This volume contains the written account of the Bonn Seminar on Arithmetic Geometry 2003/2004. It gives a coherent exposition of the theory of intersections of modular correspondences. The focus of the seminar is the formula for the intersection number of arithmetic modular correspondences due to Gross and Keating. Other topics treated are Hurwitz's theorem on the intersection of modular correspondences over the field of complex numbers and the relation of the arithmetic intersection numbers to Fourier coefficients of SiegelEisenstein series. Also included is background material on onedimensional formal groups and their endomorphisms and on quadratic forms over the ring of \(p\)adic integers. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in number theory. Table of Contents  G. Vogel  Modular polynomials
 U. Görtz  A sum of representation numbers
 U. Görtz  Arithmetic intersection numbers
 T. Wedhorn  The genus of the endomorphisms of a supersingular elliptic curve
 V. Meusers  LubinTate formal groups
 E. Viehmann and K. Ziegler  Formal moduli of formal \(\mathcal{O}_K\)modules
 S. Wewers  Canonical and quasicanonical liftings
 V. Meusers  Canonical and quasicanonical liftings in the split case
 E. Viehmann  Lifting endomorphisms of formal \(\mathcal{O}_K\)modules
 I. Vollaard  Endomorphisms of quasicanonical lifts
 I. Bouw  Invariants of ternary quadratic forms
 M. Rapoport  Deformations of isogenies of formal groups
 S. Wewers  An alternative approach using ideal bases
 T. Wedhorn  Calculation of representation densities
 M. Rapoport and T. Wedhorn  The connection to Eisenstein series
 Index
