  For spectral problems, determined by ordinary differential equations, we
consider finite-gap potentials as exact solvable by quadratures in the spirit
of the Picard--Vessio theory and suggest that this class is the only one.
Ideology goes back to works by Drach 1919 but has not been mentioned in the
modern literature. We exhibit new examples and technique for obtaining
necessary ingredients of exact integrability: new formula for the
$\Psi$-function, main trace formula and problem of inversion of Abelian
integrals.
