N¿n models were invented by A. N¿n in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithmeticians and algebraic geometers have applied the theory of N¿n models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about N¿n models, and even to go back to the basics of their construction. The authors have taken this as their incentive to present a comprehensive treatment of N¿n models. This volume of the renowned ", Ergebnisse", series provides a detailed demonstration of the construction of N¿n models from the point of view of Grothendieck's algebraic geometry. In the second part of the book the relationship between N¿n models and the relative Picard functor in the case of Jacobian varieties is explained. The authors helpfully remind the reader of some important standard techniques of algebraic geometry. A special chapter surveys the theory of the Picard functor.