The twin squares of piazza Maggiore and piazza del Nettuno form the heart of the city. Home to a number of impressive, medieval palazzi (many of which now house designer boutiques), as well as the ornate Neptune fountain, which is the city’s symbol, these squares are the centre of Bologna’s social life.

The city’s progressive legacy is recalled on the wall outside the Sala Borsa in piazza del Nettuno, in a stark but impressive assemblage of black and white photographs of Bolognese partisans who were killed by fascists during World War II. Nor did Bologna stop paying for its beliefs after the war. Right-wing terrorists killed nearly 100 people when they blew up the central train station in 1980.

The city’s imposing, unfinished cathedral, the Basilica di San Petronio, is at the southern end of piazza Maggiore. Started in 1390, it’s the fifth-largest church in the world, and its main entrance contains a striking collection of bas-reliefs by the 15th-century artist Jacopo della Quercia. Inside is Italy’s oldest organ, an enormous sundial and frescoes illustrating scenes from Dante’s Divine Comedy in the Cappella dei Re Magi.

On either side of the basilica are the Palazzo dei Notai, which housed the medieval jurists who became the architects of European law, and the Museo Civico Archeologico (via dell’Archiginnasio 2, 051 275 7211, closed Mon), noted for its Etruscan treasures. Attached to the museum is the Archiginnasio, Europe’s oldest surviving university. Through the arches of via dell’Archiginnasio lies a warren of narrow streets lined with food shops.

Many of Bologna’s food shops are pure theatre, and the owners won’t mind if you linger. The most famous is Tamburini (via Caprarie 1, 051 234 726, closed Sun), a masterpiece of presentation outside which a nun or monk sits every day collecting alms. But even greater entertainment – and marvellous food – can be had at La Salumeria da Bruno e Franco (via Oberdan 16, www.la-salumeria.it), a quick stroll south of piazza Maggiore. There Franco, Arrigo and the younger Lorenzo are kitted out in red berets and bow ties as a constant stream of customers rolls up to buy beautifully presented delicacies.

One famous son of the city who gorged a little too much on tortelloni was the corpulent opera composer Giacomo Rossini, who studied at the Conservatorio Martini (piazza Rossini 2, 051 221 483, museum closed Sat, Sun). Many of his original scores and manuscripts are displayed in the library. The lovely San Giacomo Maggiore church (051 225 970) is decorated with 15th-century frescoes by Lorenzo Costa. On the other side of the university is Bologna’s fine art collection, the Pinacoteca Nazionale (via delle Belle Arti 56, 051 420 9411, closed Mon), with works by the city’s Renaissance painters and by master Raffaello; look out for the intense, brilliantly colourful work of the 14th-century artist Vitale da Bologna.

• Tourist information: Palazzo Podestà, piazza Maggiore 1 (051 246 541, www.bolognaturismo.info).