The Bute and the Randolph Halls were built 1878-1884. They were designed by Sir George Gilbert Scott (1811-1878), but he died soon after completing his drawings and the plans were executed by his son John Oldrid Scott (1841-1913) and Edwin Morgan. The Bute Hall was named for John Patrick Crichton-Stuart, 3rd Marquess of Bute, who gifted the funds for its construction.
The halls were restored in 1986. Analysis of the paint layers found that the original decoration was based on heraldic colours of the Marquis of Bute - red, blue, silver and gold. The inspiration for the cross, thistle and fleur de lys motifs was also confirmed as having been chosen in honour of the Marquis. The Glasgow Herald report of the opening event in 1884 reported that "the iron columns, ... are intended to receive as appropriate enrichment a diaper [repeated pattern] formed of the heraldic badges appertaining to the Marquis of Bute".
The stained glass windows consist of five installations created in memory of:
- Alexander McGrigor LLD of Cairnoch, who was Dean of Faculties (18761-1879) and a member of the University Court as Rector's Assessor (1884-1887). Window designed by Sir Edward Coley Burne-Jones (1833-1898).
- John Caird, MA, DD, LLD, successively student (1837-1845), Professor of Theology (1862-1873) and Principal and Vice-Chancellor (1873-1898). Window designed by Henry Dearle (1860-1932).
- John Pringle Nichol, LLD, Professor of Astronomy (1836-1859), John Nichol, Professor of English Language and Literature (1862-1889) and Agnes Jane Nichol (or Jack) (1837-1901). Window designed by Henry Holiday (1839-1927).
- Robert Story, Professor of Ecclesiastical History (1886-1898) and Principal (1898-1907). Window designed by Douglas Strachan (1875-1950).
- Janet Anne Galloway, Honorary Secretary of Queen Margaret College (1883 to 1909). Window designed by Douglas Strachan (1875-1950).
The figures in the windows represent a wide range of characters and subjects including writers, philosophers, scientists, theologians, saints, monarchs and women.
The Principal Staircase leads to the Randolph Hall, which serves as an anteroom for the larger Bute Hall and is separated by a screen.