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The greatest free museum in Italy! There’s a bit of everything: paintings by the likes of Bellini and Mantegna, a stupendous cycle of 16th-century tapestries, archaeological collections and, its greatest piece, Michelangelo’s achingly unfinished Rondanini Pietà .

Among the top pieces in this small archaeological collection, which traces Lombard and neighbouring civilizations from prehistory to the end of the Roman era, is the Trivulzio Cup. This precious 4th-century glass cup has a delicate glass netting hovering just above the chalice surface on thin stilts of glass, along with a raised inscription that reads “Drink to Enjoy Long Life”.

Milan’s gallery of modern art is among the best in Italy. The works concentrate on Italian artists of the 20th century, including De Chirico, Modigliani and Boccioni. The collection is housed in the Palazzo Reale. The museum underwent restoration in 2004. Call ahead to confirm opening hours.

We can thank Napoleon’s penchant for looting the art of his conquered territories for the existence of the Carrara, named after the count who, in 1795, stewarded the emperor’s collection. Pillaged from across Northern Italy, in its ranks are works by Botticelli, Raphael, Bellini, Mantegna, Canaletto, Carpaccio, Guardi and Tiepolo. Above all, though, come to admire the emotion-filled Renaissance paintings of Lorenzo Lotto, a Venetian painter who settled in Bergamo in 1513.

Though there are Romanesque carvings and detached frescoes galore in the cloisters, chapels and chambers of this medieval monastery, the real focus here is on Brescia’s great era as a Roman colony, and the archaeological works on display are astoundingly beautiful, numerous and well-preserved.

Had Leonardo possessed more technological ambition, we might have had working versions of his helicopters, water screws, gatling guns, parachutes and siege engines over four centuries ago. As it is, we can make do with the (modern) wooden mock-ups on display at this science and technology museum, alongside instructive exhibits on physics and antique autos and aeroplanes.

Poldi-Pezzoli’s Milanese mansion is preserved as a monument to his collections, from Persian tapestries, ancient arms and armour to historic jewellery and, above all, art. In one room alone, there are paintings by Piero della Francesca, Giovanni Bellini, Mantegna and Botticelli.

If it has to do with the opera in Milan, it’s on display here. It’s an odd collection, from costumes worn by Nureyev or Callas to historic musical instruments, and from Verdi’s death mask (and some of his original scores) to Toscanini’s batons.

This formidable mix of Old Masters was started by Cardinal Frederico Borromeo as an adjunct to the Ambrosiana Library. Famously, the library is home to the Codex Atlantico , which contains the lion’s share of Leonardo’s drawings and sketches – photocopied pages from it are displayed in the Pinacoteca. Elsewhere, you’ll find paintings by Botticelli, Titian and Caravaggio, as well as Raphael’s giant preparatory sketch for the School of Athens .

Lombardy’s most important painting gallery, displaying works by Mantegna, Giovanni Bellini, Piero della Francesca, Caravaggio, Tintoretto, Veronese, Coreggio, Lotto, Carpaccio, Tiepolo, El Greco and Rembrandt.