Between 1932 and 1937, Landau headed the Department of Theoretical Physics at the National Scientific Center Kharkiv Institute of Physics and Technology, and he lectured at the University of Kharkiv and the Kharkiv Polytechnical Institute. Apart from his theoretical accomplishments, Landau was the principal founder of a great tradition of theoretical physics in Kharkiv, Ukraine, sometimes referred to as the "Landau school". In Kharkiv, he and his friend and former student, Evgeny Lifshitz, began writing the Course of Theoretical Physics, ten volumes that together span the whole of the subject and are still widely used as graduate-level physics texts. During the Great Purge, Landau was investigated within the UPTI Affair in Kharkiv, but he managed to leave for Moscow to take up a new post.
In 1932, Landau computed the Chandrashekhar limit; however, he did not apply it to white dwarf stars.