The madrasa is the college of Islamic law, and in its classical form it was as much a legal and financial arrangement as a building, brought into being by the endowment that paid for it.
Chair, stipend, students
In the classical period the madrasa was a specific institutional form: a building endowed as a waqf, with a professor holding a stipended chair in a particular school of law, students supported by the same endowment, and a curriculum centred on jurisprudence and the sciences that serve it. The endowment fixed the whole arrangement in perpetuity, naming the subject, the school and often the family from whom the teachers were to be drawn, so the college depended on private charitable capital rather than on a state.
Spread and transformation
From the eleventh century the model spread across the Islamic world, the Nizamiyya colleges of the Seljuk lands being the celebrated early examples, and it became the principal institution of higher religious learning from Morocco to Central Asia. In the modern period the word has broadened to cover schools of many kinds, and state education systems have absorbed or displaced much of the older endowed structure, so that a term once denoting a precise endowed law college now names religious schools of very different character, a shift that mirrors the fate of the waqf that founded them.