We shall consider different 1 D models: Bose gas with delta interaction, spin chains and strongly correlated electrons [Hubbard model]. The models became interesting lately, because of experimental progress: optical lattices and ARPES in highly anisotropic crystalline structures. Understanding of dynamics of these models goes beyond perturbation theory or numerical analysis. We can solve the models exactly by Bethe Ansatz. We will construct the ground state and excitations. We shall evaluate dispersion curve and calculate scattering matrix, correlation functions, magnetization curve and thermodynamics. We shall also consider quasi-classical limit.