A complex number is called algebraic if it is a root of a non-constant polynomial with integer coefficients and is transcendental otherwise. Over recent decades, the transcendental nature of special values of certain arithmetic functions which verify functional equations has been a fascinating branch of Number Theory and attracts an incredible number of work. However, beautiful mysteries remain unsolved.

This CIMPA school aims to familiarize graduate students and young researchers to basic concepts and tools of Differential Galois Theory, Diophantine Geometry, Transcendental Number Theory and introduce them to some beautiful theorems about the transcendence of values of particular functions such as the modular j-function, zeta functions, M-functions.

Three introductory courses and three advanced courses will be given by leading experts in their fields. It will be suitable for motivating participants to gain entry into the theory and to discover some of the cutting-edge research problems in Modern Number Theory.