Complex sentence: After German troops had been dislodged from Warsaw, classes started in improvised conditions on 22 January 1945, and by the end of the year all the pre-war faculties were re-opened.
Split into simpler sentences: After German troops were dislodged from Warsaw, classes started in improvised conditions on 22 January 1945. By the end of the year, all the pre-war faculties were re-opened.