Completed in 1897, Altgeld Hall, originally known as the Library Building, was designed by Nathan Ricker and James McLaren White. It originally served as the University Library with from its inauguration in 1897 until 1927, with the library occupying the ground floor, a museum in the basement and stacks and offices on the second floor. In 1927, the School of Law moved into the building where they resided until 1955, when they received their own building. The North entrance of the building still bears the title "Law Building". From 1955 to the present, the Department of Mathematics and the Mathematics Library have called the building home.
The building is an example of Richardsonian Romanesque architecture and the external stonework is pink limestone. The original pink hue may still be seen in the interior of the East entrance. The intricate murals in the modern library room were painted by Newton A. Wells. Four major additions in 1915, 1918, 1925, and 1927 expanded the building to its present proportions.
The building was renamed in the 1940's in honor of former Governor John Peter Altgeld. Altgeld, who "received no formal education until joining the Union Army in 1863", was the primary driving force behind the creation of a library at the University. He lobbied for a Tudor-Gothic style for the new building, but President Andrew Sloan Draper pushed for Romanesque design of Ricker, stating, "the motif and essence of [Tudor-Gothic] was military defense, not education and generosity".
Several class gifts reside in and around Altgeld Hall. Directly in front of the building rests the second oldest class memorial on campus, a boulder inscribed "Class of '76", from the class of 1876. Above its North entrance hangs a lantern emblazoned with the numerals of the class of 1905. The bell carillon in the chimes tower was cast in 1920 by the McShane Bell Foundry  and was purchased through a long stream of class gifts. The classes of 1914 and 1921 purchased a Westminster clock to strike the hours and quarter hours on the chimes, while the class of 1922 purchased the bronze tablet at the base of the tower.
Altgeld Hall was added to the National Register of Historic Places in 1970.