Periods of hyperelliptic integrals expressed in terms of $\theta$- constants by means of Thomae formulae

The expressions for the periods of first and second type integrals on hyperelliptic curve are given in terms of $\theta$-constants. The principal tool of the derivation are Thomae formulae which link theta constants with branching points. Another ingredient of the derivation is the Picard-Fuchs equations for the hyperelliptic periods. The talk will survey some basic results in the theory of hyperelliptic functions.