Printing had been undertaken in Cambridge in the 1520s and a Royal charter in 1534 gave to the University the power to name (or license) three printers (stationers) who were to print and publish works which it approved. Another fifty years were to pass before this privilege was regularly exercised and it eventually developed into the University Press. From 1584, regular publication began under the University's privilege and continued more or less steadily but did not achieve real force until Richard Bentley's reorganisation in the last decade of the seventeenth century provided new premises and types. These improvements allowed the University Press in due course to exploit more fully the monopoly of Bible printing which it shared with Oxford and the 'King's Printers', and to produce a steady stream of works essential to the development of its studies. The Cambridge University Press continues to this day as one of the oldest and largest academic publishers in the world.

The mathematical work of the seventeenth century had developed its full flower in the career of Sir Isaac Newton (1643-1727), who with his followers pursued scientific investigations of all sorts. This is reflected in the rapid establishment by the University and by private donors of a series of professorships for mathematics (the Lucasian), chemistry, astronomy (the Plumian), anatomy, botany, geology (the Woodwardian), astronomy and geometry (the Lowndean), and experimental philosophy. The professors encouraged the provision of teaching aids within the University: this is the time when the Botanic Garden and the Woodwardian Museum of Fossils were established through private donations, and an Observatory was set up by Trinity College. Parallel with this scientific activity, two professorships of Arabic (Sir Thomas Adams and the Lord Almoner's), moral philosophy (the Knightbridge), music, modern history (Regius), divinity (Norrisian) and law (Downing) were established to meet other needs.

The disputations and opponencies of the past were adapted to the new studies. Those completing the first stages of their graduation were arranged in an order of merit, which was announced on Ash Wednesday. Entertaining verses, sometimes satirical, were read at the graduation ceremony by a senior BA (or 'old bachelor') sitting, as a licensed fool, on a three-legged stool or tripod. In time, the graduation list came to be printed on the back of these Tripos verses, and became known as the Tripos list.

Despite the provision for natural sciences and arts, from the late 17th century, mathematics came to dominate studies in Cambridge, and eventually 'the Tripos' came to mean the examination in mathematics. This was conducted in the Senate-House, where candidates likely to do well took special papers of 'problems', at first dictated to them by the moderators but by 1800 appearing as a printed paper.

The University Library had expanded with the rest of the University during the later seventeenth century, and after the gift by George I of the manuscripts and books of Bishop John Moore, it outgrew its original quarters in the Old Schools. Plans had already been suggested for the building of a Senate-House in front of the Old Schools, and this was finally completed in 1730. Between this date and 1758 a series of alterations and adaptations to the old buildings provided space and splendid fittings for the Library, which are familiar from Rowlandson's drawings: many of the cases survive in the present University Library.

Additions to the staple mathematical curriculum were only slowly made: an examination for the LLB in civil law appeared first in 1816, a classical Tripos began in 1824 and, after 1843, ordinands could take a voluntary examination in theology which was to develop into a theological Tripos.

These changes began during a time when the central administration of the University was strengthened and extended by a series of small reforms which were to be fundamental to future changes. The Statutes, for example, were for the first time issued in a printed version in 1785, and the system of permanent or temporary committees (usually termed syndicates) expanded to cover the supervision of estates (which the endowments of the new professorships had greatly extended), and also of buildings and institutions such as the Botanic Garden, the Library and the Press.