The purpose of this book is to give an introduction to Arakelov theory. This theory consists in transposing results of algebraic geometry,
especially numerical results, to the number field case, by completing the set of points (or divisors) to include those at infinity, that is, the archimedean places. This is done by considering hermitian structures in addition to sheaf structures, so analysis becomes number theory at infinity.
One can then get the analogous results in a number of cases.