This was originally the main university building, and today is home to the Geography and History faculties. It was built in the final third of the 18th century based on plans by Miguel Ferro Caaveiro. It was modified at the end of the 19th century. It is constructed of granite masonry with two tiled roof slopes and built on a square layout organised around the cloisters.

The facade is divided into two parts (the third part is at the back) for those entering and those leaving in order to give a feeling of movement. It is presided over by the entrance stairs and the entrance itself. The entrance is marked by four large Ionic columns that include both parts of the facade and which used to support a pediment topped with a figure of Minerva by Ferreiro (now in the Chemical Science faculty), and which now bears the crest.

The current scene is topped by the statues of the benefactors of the university from different times in its history: Juan de Ulloa, the Count of Monterrei, Álvaro de Cadaval and Gómez de Marzoa. The third part features medallions showing Diego de Muros and Alonso de Fonseca and a relief of Wisdom crowning studious youth.