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The historic centre is a small, circular zone contained within a ring-road that connects the city's ancient defensive "doors". Four wide thoroughfares divide the area and meet in the middle at piazza del Duomo, home to Milan's magnificent cathedral (1). From here, all the main sights are within walking distance: the Galleria Vittorio Emanuele (2) and La Scala (3) to the north; CastelloSforzesco (4) just north-west; the ineffably stylish designer district half a mile north-east; and the awesome basilica of Sant'Ambrogio directly west (5). Two metro lines (1 and 3) stop at piazza del Duomo and tickets, which cost €1 (70p) for all destinations, can be bought at any newspaper kiosk. For a map of the city and information about other interesting areas, visit the Tourist Office (6) on the corner of piazza del Duomo and via Marconi (00 39 02 7252 4301, www.milanoinfotourist.com). The office is open Mon - Sat, 8:45am - 6pm and on Sun, 9am - 5pm, with an hour's closure 1pm-2pm every day.
From piazza del Duomo, head north-west along via Mercanti, pausing to acknowledge Palazzo della Ragione (7), an eye-popping medieval governmental building, on the way. Cross piazza Cordusio and turn left when you get to via Meravigli which becomes corso Magenta, one of Milan's smartest and most interesting streets. Continue past palazzo Litta at number 24 (8), a marvellous example of rococo exuberance, and a series of stylish fashion boutiques, to the church of Santa Maria delle Grazie (9), just after via Caradosso, where Leonardo da Vinci's Last Supper adorns the refrectory wall (00 39 02 8942 1146, open Tuesday to Sunday 8:15am-6:45pm). The entrance fee is €6.50 (£4.60) although booking is essential, adding an extra €1.50 (£1) to the cost of the ticket. From there, walk south down via Zenale to via San Vittore and the Museum of Science and Technology (10) at via San Vittore 21 (00 39 02 485 551, www.museoscienza.org). Open Tuesday to Sunday 9:30am-5pm, entrance is €7 (£5). Stop here to admire two glorious cloisters by Bramante. Then stroll south-east down via San Vittore, grab a slice of pizza at the excellent panetteria Sant'Ambrogio (11), followed by a tour of the astounding 4th-centruy Basillica of Sant'Ambrogio. (see map for route.)