De Branges spaces and canonical systems

In this talk we give a survey of the basics of the de Branges spaces' theory and its applications to the spectral theory of canonical systems of differential equations. We plan to discuss the following topics: special classes of canonical systems, generalized Fourier transform, axiomatic and analytic description of de Branges spaces, ordered structure of subspaces in de Branges spaces, inverse spectral theorem for canonical systems.