Schottky model of Riemann surfaces and efficient variational formulae

Schottky uniformization of Riemann surfaces had been used for the efficient calculations with the surfaces and their moduli since the end of 1980-ies. I will give a review of this model and related computational algorithms. To efficiently solve various equations in the moduli spaces one needs explicit formulae relating variations of function theoretic objects like abelian integrals to the variations of the group generators. Formulae of this kind were suggested by the author in 1997 and their computer implementation is based on another remarkable formulae invented by D.Hejhal yet in mid 1970-ies.