Short answers, pulled from the story.
The University of Berlin was established by King Friedrich Wilhelm III on the 16th of August 1809 and admitted its first students on the 6th of October 1810, with the first semester beginning on the 10th of October 1810. The university received its current name, Humboldt-Universitat zu Berlin, in 1949.
The university was founded on the initiative of Wilhelm von Humboldt, a liberal Prussian philosopher and linguist, together with Johann Gottlieb Fichte and Friedrich Daniel Ernst Schleiermacher, at the direction of King Friedrich Wilhelm III.
Humboldt University of Berlin is associated with 57 Nobel Prize laureates among its past and present faculty and alumni, the most of any German university.
On the 10th of May 1933, some 20,000 books taken from the university's library were burned at the Opernplatz square, now known as Bebelplatz, in a demonstration protected by the SA and accompanied by a speech from Reich Minister of Propaganda Joseph Goebbels. A monument called The Empty Library, a subterranean white room visible through a glass panel in the pavement, now marks the site.
The Freie Universitat Berlin was established in West Berlin in 1948 with support from the United States after Soviet occupiers imposed ideological controls on the original University of Berlin, including requiring lectures to be approved by Socialist Unity Party officials and arresting dissident students. Its name was a deliberate contrast to what western observers called the unfree communist-controlled institution in East Berlin.
The Humboldtian model centers on the union of teaching and research in the work of the individual scholar or scientist, rather than the transmission of established knowledge alone. It became a model for European and Western universities and influenced institutions including Johns Hopkins University.