The model has many names: Lieb-Liniger, Bose gas with delta interaction and nonlinear Schroedinger. A limiting case is called Tonks-Girardeau. It is solvable by algebraic Bethe ansatz. We shall use notations of quantum inverse scattering method. Applications will be mentioned. ----- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed.