In the footsteps of Galois, we shall try to recover arithmetic properties from Galois theoretic data. In particular, we shall analyse what arithmetic information about a field K is encoded in its absolute Galois group G(K), i.e., the Galois group of a separable closure of K over K. This is the universal Galois group over K in the sense that every other Galois group over K is a quotient of G(K). It is by now well known that for real closed or p-adically closed fields, G(K) "knows everything" about the arithmetic of K. More recently, it was established that if K is the field of rational numbers, then G(K) knows "almost everything" - we shall make this precise and indicate main steps for the proof during the talk.