The origin of inverse spectral problems lies in natural science, but the problems themselves are purely mathematical. At the beginning these problems attracted attention of mathematicians by their nonstandard physical contents. But we think that today their place in mathematical physics is determined rather by the unexpected connection between inverse problems and nonlinear evolution equations which was discovered in 1967. This discovery was made in a famous paper by Gardner, Greene, Kruskal and Miura (1967). They found that the scattering data of a family H(t) (−∞ < t < ∞) (i.e. the reflection coefficients r(k, t) and normalizing coefficients m(ik l , t)) of Schrodinger operators satisfy linear differential equations if the potentials u(x, t) are rapidly decreasing solutions of the KdV equation (1) .