In addition to Copernicus, the university's notable alumni include heads of state King John III Sobieski, Pope John Paul II, and Andrzej Duda; Polish prime ministers Beata Szydło and Józef Cyrankiewicz; renowned cultural figures Jan Kochanowski, Stanisław Lem, and Krzysztof Penderecki; and leading intellectuals and researchers such as Hugo Kołłątaj, Bronisław Malinowski, Carl Menger, Leo Sternbach, and Norman Davies.

Four Nobel laureates have been affiliated with the university, all in literature: Ivo Andrić and Wisława Szymborska, who studied there, and Czesław Miłosz and Olga Tokarczuk, who taught there.

In the mid-14th century, King Casimir III the Great realised that the nation needed a class of educated people, especially lawyers, who could arrange a better set of the country's laws and administer the courts and offices.

His efforts to found an institution of higher learning in Poland were rewarded when Pope Urban V granted him permission to set up a university in Kraków.

Development of the University of Kraków stalled upon the death of Casimir III, and lectures were held in various places across the city, including, amongst others, in professors' houses, churches and in the cathedral school on the Wawel Hill.

[8][10] The faculties of astronomy, law and theology attracted eminent scholars: for example, John Cantius, Stanisław of Skarbimierz, Paweł Włodkowic, Jan of Głogów, and Albert Brudzewski, who from 1491 to 1495 was one of Nicolaus Copernicus' teachers.

This rapid expansion in the university's faculty necessitated the purchase of larger premises in which to house them; it was thus that the building known today as the Collegium Maius, with its quadrangle and beautiful arcade, came into being towards the beginning of the 15th century.

At this time, the Collegium Maius consisted of seven reading rooms, six of which were named for the great ancient scholars: Aristotle, Socrates, Plato, Galen, Ptolemy, and Pythagoras.

This phenomenon was recorded as part of a more general economic and political decline seen in the Polish–Lithuanian Commonwealth, which was suffering from the effects of poor governance and the policies of hostile neighbors at the time.

[12] The Austrians were in many ways hostile to the institution and, soon after their arrival, removed many of the furnishings from the Collegium Maius' Auditorium Maximum in order to convert it into a grain store.

Thereafter the Austrian authorities took on a new role in the development of the university and provided funds for the construction of a number of new buildings, including the neo-gothic Collegium Novum, which opened in 1887.

[14] Nevertheless, it was in the Grzegórzecka and the Kopernika areas that much of the university's expansion took place up to 1918; during this time the Collegium Medicum was relocated to a site just east of the centre, and was expanded with the addition of a number of modern teaching hospitals – this 'medical campus' remains to this day.

Now a major centre for education in the independent Republic of Poland, the university attained government support for the purchase of building plots for new premises, as a result of which a number of residencies were built for students and professors alike.

The library's monumental building, construction of which began in 1931, was finally completed towards the end of the interwar period, which allowed the university's many varied literary collections to be relocated to their new home by the outbreak of war in 1939.

Construction work proved slow and many of the stated goals were never achieved; it was this poor management that eventually led a number of scholars to openly criticise the government for its apparent lack of interest in educational development and disregard for the university's future.

The scientists and physicians from the Collegium Medicum carry out pioneer studies, e.g. in cardiac surgery, urology and neurology, often leading to the development of novel treatment methods.

UJ archaeologists lead explorations of ancient sites in various parts of the world, including Egypt, Cyprus, Central America, South Asia and Altay.

The library also has an extensive collection of underground political literature (so-called drugi obieg or samizdat) from Poland's period of Communist rule between 1945 and 1989.

After 1775, during the reforms of Komisja Edukacji Narodowej, which established the first Ministry of Education in the world, various small libraries of the university were formally centralised into one public collection in Collegium Maius.