The University of Sheffield (informally Sheffield University or TUOS) is a public research university in Sheffield, South Yorkshire, England. Its history traces back to the foundation of Sheffield Medical School in 1828, Firth College in 1879 and Sheffield Technical School in 1884. The University College of Sheffield was subsequently formed by the amalgamation of the three institutions in 1897 and was granted a royal charter as the University of Sheffield in 1905 by King Edward VII.

Sheffield is formed from 50 academic departments which are organised into five faculties and an international faculty. The annual income of the institution for 2023–24 was £887.9 million, of which £185.8 million was from research grants and contracts, with an expenditure of £651.4 million. Sheffield is regarded as one of the top engineering universities in Europe. As of the latest HESA statistics, it had the highest engineering research income and expenditure among all the universities in the UK for two consecutive years.

The university is one of the original red brick universities and a founding member of the Russell Group. It is also part of the Worldwide Universities Network, the N8 Group of the eight most research intensive universities in Northern England and the White Rose University Consortium. According to the latest Research Excellence Framework 2021, Sheffield is ranked 11th in the UK for research power calculated by multiplying the institution's GPA by the total number of full-time equivalent staff submitted.

There are six Nobel laureates affiliated with Sheffield, as either the alumni or former long-term staff of the university. They are contributors to the development of penicillin, the discovery of the citric acid cycle, the investigation of high-speed chemical reactions, the discovery of introns in eukaryotic DNA, the discovery of fullerene, and the development of molecular machines. Alumni also include several heads of state, Home Secretaries, Court of Appeal judges, Booker Prize winners, astronauts and Olympic gold medallists.

The University of Sheffield was originally formed by the merger of three local institutions: the Sheffield School of Medicine, Firth College, and the Sheffield Technical School. With a history dating back to as early as the 1810s, the Sheffield School of Medicine is the university's oldest predecessor institution, which is also the oldest higher education establishment in Sheffield. In 1795, the General Infirmary was opened, becoming the first hospital in the city. Because of the apprenticeship-type training, the medical education at that time was largely unstructured. Regarded as the father of Sheffield's medical education, surgeon apothecary Hall Overend began to train medical students in 1811. His school of anatomy and medicine was externally recognised in 1828, and he conducted and taught human dissection in an anatomy museum at his home in Church Street. Overend, however, was not officially registered as a lecturer with the Society of Apothecaries, a recognised body for medical education. Physicians and surgeons of the General Infirmary suggested that a school associated with the hospital would be highly eligible for recognition by the society. As a result, in 1828, a public meeting was called by physician Sir Arnold Knight, and supported by Overend, to establish a new medical school. The Sheffield Medical Institution was formally opened a year later in 1829 on Surrey Street, with the Latin motto Ars longa vita brevis (Art is long, life is short), which refers to the difficulty to acquire and practice the art of Medicine. Knight laid the foundation stone and delivered the opening lecture.

The University Extension Movement emerged in the 1870s with the aim of providing education in the city which lacked any tertiary institutions. During the period, the steel industry in Sheffield was prospering and the city's population was doubled to around 240,000 from the 1840s. In 1871, the university extension scheme arrived in Sheffield, and a group of lecturers from the universities of Oxford and Cambridge travelled to the city giving lectures and educating people about the benefits of tertiary education. Steel manufacturer and former mayor of Sheffield Mark Firth and clergyman Samuel Earnshaw therefore organised courses in English literature and political economy. The courses became popular so Firth decided to donate £20,000 and purchase a site in the city centre (now Leopold Street and West Street) in 1877 to build a new institution for the classes. Firth College was founded during Firth's late year in 1879 and developed out of the Extension Movement scheme to teach arts and pure science subjects. The college saved the medical school, which had an insecure early history, from collapse and took over the teaching of all background subjects to medical students. In 1888 the medical school was relocated, opposite Firth College, to a new building on Leopold Street.

Firth College also helped to fund the opening of the Sheffield Technical School in 1884 to teach applied science, the only major faculty the existing colleges did not cover. The Sheffield Technical School was created by collecting funds within Firth College because of local concern about the need for technical training, particularly steelmaking in Sheffield. Former mayor of Sheffield Sir Frederick Mappin started to fundraise for the school and £10,240 was raised. A grant was secured in 1883 to fund a professor of Metallurgy and Mechanical Engineering. Many of the steel-making firms in Sheffield contributed to funding the Technical School, and research from the school in turn helped develop new processes and products for the companies. The Technical School was originally founded as a new technical department in Firth College, and in 1886, the school moved to St George's Square (later renamed Charlotte Street and now Mappin Street) on the site of the old Grammar School. William Ripper was appointed as Head of Mechanical Engineering at Firth College from 1889, then Principal of Sheffield Technical School.

Sheffield was at that time the only large city in England without a university. William Mitchinson Hicks, who was Principal of Firth College from 1892 to 1897, had an ambition to establish a university in the city. As a first stage of his ideal, Hicks was devoted to the union of the three higher education institutions in Sheffield and to transform Firth College into a university college. He also extended the college by creating new departments and adding new buildings. In 1897, Firth College merged with the Medical School and the Technical School to form the University College of Sheffield, and Hicks served as its first principal. Six years since the foundation of the university college, on 18 May 1903, the resolution to apply for a royal charter was passed. The university college started to develop its estate soon after: Western House by Weston Park on Western Bank was bought and demolished in 1903 for building a new university property. A building with a traditional collegiate quadrangle (later known as Western Bank building and now Firth Court) was planned on the site. Sir Frederick Mappin later successfully sought financial support from the Sheffield City Council and appealed for public donations. In 1904, steelworkers, coal miners, factory workers and the people of Sheffield donated over £50,000 via penny donations to help found the University of Sheffield.