The University Council conducted an architectural competition for the design of the first buildings. The winner was Francis Maloney White whose 'design, with some significant modifications, became the Quadrangle. Faced with Hobart freestone though a bluestone structure. It was known during the nineteenth century as 'the University' and at various times since has housed the Central Administration, the main Library for many years, the Law Faculty, and most recently, once again, parts of the Arts Faculty. The east and west sides of the Quadrangle Building were completed by October 1855 and the imposing north wing in 1857. It was clear by this time that the Government would not provide additional money to complete the south wing - and in any case the Council was making plans for a medical school, for which a building would also be needed - but at some distance from the Quadrangle. The vaulted cloisters of the east and west wings were not added until 1930 and the quadrangle was not fully enclosed until 1969. The Quadrangle building combined private residences for the professors, teaching spaces, accommodation for the Registrar, a council chamber, examination hall, library and museum.
The armorial bearings of the members of the Buildings Committee in 1856 - Lauchlan Mackinnon (chairman), Barry, Childers, W. F. Stawell, and Francis Murphy - are incorporated in the masonry of the North wing.
The North Extension completed in 1875 included, on the ground floor, a large central room with adjoining wash rooms for students, called the Students’ Hall, a workshop for Professor Wilson and a room for Professor McCoy. The Engineering workshop was in the cellar. On the first floor was a spacious library. Long concealed by modern annexes, this section of the building was revealed again in 2003.