The University of Madras is a public state university in Chennai, Tamil Nadu, India. Established in 1857, it is one of the oldest and among the most prominent universities in India, incorporated by an act of the Legislative Council of India under the British government.

A collegiate university is a university in which functions are divided between a central administration and a number of constituent colleges. Historically, the first collegiate university was the University of Paris and its first college was the Collège des Dix-Huit. The two principal forms are residential college universities, where the central university is responsible for teaching and colleges may deliver some teaching but are primarily residential communities, and federal universities where the central university has an administrative role and the colleges may be residential but are primarily teaching institutions. The larger colleges or campuses of federal universities, such as University College London and University of California, Berkeley, may be effectively universities in their own right and often have their own student unions.