Since its birth, Model Theory has been developing a number of methods and concepts that have their intrinsic relevance, but also provide fruitful and notable applications in various fields of Mathematics. It is a lively and fertile research area which deserves the attention of the mathematical world.

This volume:
-is easily accessible to young people and mathematicians unfamiliar with logic;
-gives a terse historical picture of Model Theory;
-introduces the latest developments in the area;
-provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters.

A Guide to Classical and Modern Model Theory is for trainees and professional model theorists, mathematicians working in Algebra and Geometry and young people with a basic knowledge of logic.

Il libro tratta di metodi di crittografia e sistemi, con particolare enfasi alla teoria dei numeri. Il libro e rivolto agli studenti universitari del nuovo ordinamento che debbano seguire un corso base di teoria dei numeri e crittografia. Il volume e impostato in modo chiaro e sistematico, in modo da rendere facilmente accessibile la materia agli studenti di matematica e informatica, fornendo peraltro parecchie descrizioni di applicazioni computazionali. Non mancano tuttavia accenni storici alla crittografia e alla complessita computazionale.

The book describes 4 main topics in current model theory and updates their most recent development and applications. The 4 topics are: 1) model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; 4) model theory of real and complex exponentiation. The book addresses in particular young researchers in model theory, as well as more senior researchers in other branches of mathematics.