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The University of Cambridge (informally Cambridge University, or simply Cambridge) is a public research university in Cambridge, England. It is the second-oldest university in both England and the English-speaking world, and the seventh-oldest globally. In post-nominals the university's name is abbreviated as Cantab, a shortened form of Cantabrigiensis (an adjective derived from Cantabrigia, the Latinised form of Cambridge).

The university grew out of an association of scholars in the city of Cambridge that was formed in 1209, early records suggest, by scholars leaving Oxford after a dispute with townsfolk. The two "ancient universities" have many common features and are often jointly referred to as Oxbridge. In addition to cultural and practical associations as a historic part of British society, they have a long history of rivalry with each other.

Academically Cambridge ranks as one of the top universities in the world: first in the world in both the 2010 and 2011QS World University Rankings, sixth in the world in the 2010–2011 Times Higher Education World University Rankings, and fifth in the world (and first in Europe) in the 2010 Academic Ranking of World Universities. Cambridge regularly contends with Oxford for first place in UK league tables. In the most recently published ranking of UK universities, published by the Guardian newspaper, Cambridge was ranked first.

Graduates of the University have won a total of 61 Nobel Prizes, the most of any university in the world. Affiliates of the University have won a total of 88 Nobel Prizes as of 4 October 2010, the second most of any academic institution (after Columbia University) – the most recent one being Robert G. Edwards for the prize in physiology or medicine. Academic staff of the University won a total of 52 Nobel Prizes, second most of any academic institution (after Columbia University). In 2009, the marketing consultancy World Brand Lab rated Cambridge University as the 50th most influential brand in the world, and the 4th most influential university brand, behind only Harvard, MIT and Stanford University, while in 2011, the Times Higher Education World Reputation Rankings ranked Cambridge as the 3rd most reputable university in the world, after Harvard and MIT.

Cambridge is a member of the Coimbra Group, the G5, the International Alliance of Research Universities, the League of European Research Universities and the Russell Group of research-led British universities. It forms part of the 'Golden Triangle' of British universities.

Cambridge's status was enhanced by a charter in 1231 from King Henry III of England which awarded the ius non trahi extra (a right to discipline its own members) plus some exemption from taxes, and a bull in 1233 from Pope Gregory IX that gave graduates from Cambridge the right to teach everywhere in Christendom.

After Cambridge was described as a studium generale in a letter by Pope Nicholas IV in 1290, and confirmed as such in a bull by Pope John XXII in 1318, it became common for researchers from other European medieval universities to come and visit Cambridge to study or to give lecture courses.

Cambridge's colleges were originally an incidental feature of the system. No college is as old as the university itself. The colleges were endowed fellowships of scholars. There were also institutions without endowments, called hostels. The hostels were gradually absorbed by the colleges over the centuries, but they have left some indicators of their time, such as the name of Garret Hostel Lane.

From the time of Isaac Newton in the later 17th century until the mid-19th century, the university maintained a strong emphasis on applied mathematics, particularly mathematical physics. Study of this subject was compulsory for graduation, and students were required to take an exam for the Bachelor of Arts degree, the main first degree at Cambridge in both arts and science subjects. This exam is known as a Tripos. Students awarded first-class honours after completing the mathematics Tripos were named wranglers. The Cambridge Mathematical Tripos was competitive and helped produce some of the most famous names in British science, including James Clerk Maxwell, Lord Kelvin, and Lord Rayleigh. However, some famous students, such as G. H. Hardy, disliked the system, feeling that people were too interested in accumulating marks in exams and not interested in the subject itself.

Pure mathematics at Cambridge in the 19th century had great achievements but also missed out on substantial developments in French and German mathematics. Pure mathematical research at Cambridge finally reached the highest international standard in the early 20th century, thanks above all to G. H. Hardy and his collaborator, J. E. Littlewood. In geometry, W. V. D. Hodge brought Cambridge into the international mainstream in the 1930s.

Many of the most important scientific discoveries and revolutions were made by Cambridge alumni. These include:

• Understanding the scientific method, by Francis Bacon
• The laws of motion, by Sir Isaac Newton
• The discovery of the electron, by J. J. Thomson
• The splitting of the atom by Ernest Rutherford and of the nucleus by Sir John Cockcroft and Ernest Walton
• The unification of electromagnetism, by James Clerk Maxwell
• The discovery of hydrogen, by Henry Cavendish
• Theory of Evolution by natural selection, by Charles Darwin
• Mathematical synthesis of Darwinian selection with Mendelian genetics, by Ronald Fisher
• The Turing machine, a basic model for computation, by Alan Turing
• The structure of DNA, by Francis Crick and James D. Watson
• Pioneering quantum mechanics, by Paul Dirac

Cambridge is a collegiate university, meaning that it is made up of self-governing and independent colleges, each with its own property and income. Most colleges bring together academics and students from a broad range of disciplines, and within each faculty, school or department within the university, academics from many different colleges will be found.

The faculties are responsible for ensuring that lectures are given, arranging seminars, performing research and determining the syllabi for teaching, overseen by the General Board. Together with the central administration headed by the Vice-Chancellor, they make up the entire Cambridge University. Facilities such as libraries are provided on all these levels: by the University (the Cambridge University Library), by the departments (departmental libraries such as the Squire Law Library), and by the individual colleges (all of which maintain a multi-discipline library, generally aimed mainly at their undergraduates).

The principal method of teaching at Cambridge colleges is the supervision. These are typically weekly hour-long sessions in which small groups of students – usually between one and three – meet with a member of the university's teaching staff or a doctoral student. Students are normally required to complete an essay or assignment in advance of the supervision, which they will discuss with the supervisor during the session, along with any concerns or difficulties they have had with the material presented in that week's lectures. Lectures at Cambridge are often described as being almost a mere 'bolt-on' to these supervisions. Typically, students receive between one and four supervisions per week. However the number of supervisions varies according to subject and college, and it can often be the case that a student may receive more supervisions in one college than a student reading the same subject in another college. This pedagogical system is often cited as being unique to Cambridge and Oxford (where "supervisions" are known as "tutorials").