The Collegium Maius, part of Jagiellonian University, is the oldest surviving university building in Poland, and one of the finest examples of 15th-century Gothic architecture in the city. It's best known for its star pupil, Polish astronomer and mathematician Nicolaus Copernicus. Guided tours (from 10am) show off some of his manuscripts as well as scientific books and instruments from those times. Check out the magnificent arcaded courtyard and clock (7am to dusk) and a small temporary exhibition on science.

　　The hour-long tour includes half-a-dozen historic interiors, some rare 16th-century astronomic instruments used by Copernicus, a fascinating alchemy room, old rectors’ sceptres and, the highlight of the show, the oldest existing globe (c 1510) depicting the American continent. You’ll visit an impressive Aula, a hall with an original Renaissance ceiling, and crammed with portraits of kings, benefactors and rectors of the university (five of whom were sent to Sachsenhausen concentration camp in 1939). The treasury contains everything from copies of the 1364 university foundation papers and Jan III Sobieski’s hammered silver table to film awards (including an Oscar) given to director Andrzej Wajda.

　　English-language tours depart daily at 1pm and must be booked in advance in person, by phone or over the museum website. The courtyard can be entered free of charge. Try to visit the courtyard at 9am, 11am, 1pm or 3pm, when the 14th-century replica clock on the south side chimes and its cast of medieval characters go through their paces.