  We start discussing the group of automorphisms of the field of complex
numbers, and describe, in the special case of polynomials with only two
critical values, Grothendieck's program of 'Dessins d' enfants', aiming at
giving representations of the absolute Galois group. We describe Chebycheff and
Belyi polynomials, and other explicit examples. As an illustration, we briefly
treat difference and Schur polynomials. Then we concentrate on a higher
dimensional analogue of the triangle curves, namely, Beauville surfaces and
varieties isogenous to a product. We describe their moduli spaces, and show how
the study of these varieties leads to new interesting questions in the theory
of finite (simple) groups.
