This is the first of two talks about my PhD thesis. The focus will be about the field of moduli of a G-Galois branched cover of the projective line over the algebraic numbers. In this first talk I will introduce the topic; and explain a method that allows one to describe the ramification of the field of moduli away from the primes that divide |G|. I will show how this permits to control the field of moduli under various constraints.