The University of Vienna (German: Universität Wien, Austrian German: [univɛrsiˈtɛːt ˈviːn]) is a public research university in Vienna, Austria. Founded by Duke Rudolph IV in 1365, it is the oldest university in the German-speaking world and among the largest institutions of higher learning in Europe.

The University of Vienna is associated with 17 Nobel Prize laureates and has been home to numerous scholars of historical and academic significance, including Erwin Schrödinger, Karl Popper, Stefan Zweig, Friedrich Hayek, Gustav Mahler, Sigmund Freud, Gregor Mendel, Ludwig von Mises, among others.

The university was founded on March 12, 1365, by Rudolf IV, Duke of Austria, hence the name "Alma Mater Rudolphina". After the Charles University in Prague (1347) and Jagiellonian University in Kraków (1364), the University of Vienna is the third oldest university in Central Europe and the oldest university in the contemporary German-speaking world; it remains a question of definition as the Charles University in Prague was German-speaking when founded, too. However, Pope Urban V did not ratify the deed of foundation that had been sanctioned by Rudolf IV, specifically in relation to the department of theology. This was presumably due to pressure exerted by Charles IV, Holy Roman Emperor, who wished to avoid competition for the Charles University in Prague.

The pope later granted an endowment to the university in 1365, while papal assent was finally received in 1384. This led to the University of Vienna and its Faculty of Catholic Theology being granted the status of a full university. The first university building opened in 1385. It grew into the biggest university of the Holy Roman Empire, and during the advent of Humanism in the mid-15th century was home to more than 6,000 students.

In its early years, the university had a partly hierarchical, partly cooperative structure, in which the Rector was at the top, while the students had little say and were settled at the bottom. The Magister and Doctors constituted the four faculties and elected the academic officials from amidst their ranks. The students, but also all other Supposita (university members), were divided into four Academic Nations. Their elected board members, mostly graduates themselves, had the right to elect the Rector. He presided over the Consistory which included procurators of each of the nations and the faculty deans, as well as over the University Assembly, in which all university teachers participated. Complaints or appeals against decisions of the faculty by the students had to be brought forward by a Magister or Doctor.

Being considered a Papal Institution, the university suffered a setback during the Reformation. In addition, epidemics, economic stagnation, and the first Siege of Vienna by Ottoman forces had devastating effects on the city, leading to a sharp decline in enrollment. For Emperor Ferdinand I, this meant that the university should be tied to the church to an even stronger degree, and in 1551 he installed the Jesuit Order there. As time went on, conflicts between the Jesuit school and the university arose. This led Emperor Ferdinand II, in 1623, to pass a law that incorporated the Jesuit College into the university. It was only in the mid-18th century that the Jesuits lost influence over the university and when Empress Maria Theresa ensured that the university went under the control of the monarchy. The university would later focus on the education of physicians and civil servants. Her successor Joseph II continued her reforms and further liberalized the university, abolishing official attire and allowing both Protestants and Jews to enroll by 1782, as well as introducing German as the compulsory language of instruction the year later.

Significant changes were instituted in the wake of the Revolution in 1848, with the Philosophical Faculty being upgraded into equal status as Theology, Law and Medicine. Led by the reforms of Leopold, Count von Thun und Hohenstein, the university was able to achieve a larger degree of academic freedom. The current main building on the Ringstraße was built between 1877 and 1884 by Heinrich von Ferstel. The previous main building was located close to the Stuben Gate (Stubentor) on Iganz Seipel Square, the current home of the old University Church (Universitätskirche) and the Austrian Academy of Sciences (Österreichische Akademie der Wissenschaften). Women were admitted as full students in 1897, although their studies were limited to Philosophy. The remaining departments gradually followed suit, although with considerable delay: Medicine in 1900, Law in 1919, Protestant Theology in 1923, and finally Roman Catholic Theology in 1946. Ten years after the admission of the first female students, Elise Richter became the first woman to receive habilitation, becoming professor of Romance languages in 1907; she was also the first female distinguished professor.

In the late 1920s, the university was in steady turmoil because of anti-democratic and anti-Semitic activity by parts of the student body. Professor Moritz Schlick was killed by a former student while ascending the steps of the university for a class. His murderer was later released by the Nazi regime. Following the Anschluss, the annexation of Austria into Greater Germany by the Nazi regime, in 1938 the University of Vienna was reformed under political aspects, and a huge number of teachers and students were dismissed for political and "racial" reasons. In April 1945, the then 22-year-old Kurt Schubert, later acknowledged doyen of Judaic Studies at the University of Vienna, was permitted by the Soviet occupation forces to open the university again for teaching, which is why he is regarded as the unofficial first rector in the post-war period. On 25 April 1945, however, the constitutional lawyer Ludwig Adamovich senior was elected as the official rector of the University of Vienna.