Abstract: Problems, connecting with manifolds of rational curves, have a very long hystory ,going back to classical results of Pluecker Sofus Lie and  Eli Cartan. One of the first problems is the problem of conditions on a family curves to be isomorphic to the family of lines. The new interest to such manifgolds is connecting with curved integral geometry  and the integration of nonlinear differential equations by the inverse problem method. I will give an elemntary introduction to the construction of soliton solutions using manifolds of rational curves.