Republic Square and the Kalemegdan Ridge in Belgrade

Belgrade sits on a ridge where the Sava runs into the Danube, and almost everything old in the city clings to that ridge. This route starts in the flat, busy middle of town and climbs gradually to the edge, where the fortress looks over both rivers.

On the way you pass a museum, a mosque and a cathedral that belong to very different centuries, then spend the second half among the ramparts and park paths of Kalemegdan. Wear shoes for cobbles and gravel.

Begin on Republic Square, in front of the National Museum of Serbia. The building dates from 1902–1903 and was put up as a financial institution's headquarters, which is why it looks more like a bank than a gallery. The collection inside runs from the Lady of Vinča, a prehistoric figure, to the Miroslav Gospels of 1186, and later French and Dutch painting. Take a moment outside to find the Prince Mihailo monument on the square.

Turn off the main street into Gospodar Jevremova and you reach the Bajrakli Mosque. Belgrade once had 273 mosques; this is the only one left from the Ottoman centuries. Look at the plain cube topped by a single dome, and at the thin minaret on its corner. Under the Austrians in the early 1700s it served as a Catholic church, and it was reopened for Muslim worship in 1868. Stay outside, or enter only where a notice invites visitors, and dress modestly.

The Cathedral Church of St. Michael the Archangel was built between 1837 and 1840 and consecrated in 1845, in the calm, classical style of the early Serbian state. It was the church of the princes of that period, and Prince Miloš Obrenović is buried here, as are the language reformer Vuk Karadžić and the writer Dositej Obradović. Step in for the carved and gilded iconostasis by Dimitrije Petrović, and look at the faces of the icons painted by Dimitrije Avramović.

You are now at the edge of Kalemegdan park. The Military Museum stands inside the fortress, and its paths are lined with tanks, howitzers and armoured cars, some of them captured from retreating Axis forces in 1944. The museum itself, founded in 1878, runs from Roman helmets and medieval armour to modern weapons. If you are not a museum person, the outdoor display alone is worth a slow loop.

The Belgrade Fortress is built in two parts: the Upper Town on the level top, the Lower Town sloping to the water. Most of what you see was rebuilt by the Austrians between 1718 and 1739. Find the Roman Well, which is neither Roman nor a well in the ordinary sense, and the Despot Stefan Tower, which has housed an observatory since 1963. Then walk to the rampart edge: the Sava meets the Danube below, with the flat green island beyond.

The little church called Ružica sits in the Lower Town of the fortress. The Austrians built a gunpowder store here; the Serbs turned it into a church after the Ottomans left in 1867, and the architect Nikolay Krasnov rebuilt it between 1921 and 1925. Inside, the chandeliers and candelabra were cast from melted-down rifle bullets, shell cases and sabres. Go in and look up.

Finish at the Victor, a bronze figure by Ivan Meštrović that was unveiled on 7 October 1928. He holds a falcon in one hand and a sword in the other, for peace and war, and honours Serbia's wins in the Balkan Wars and the First World War. It was first planned as a fountain for Terazije square, and some critics objected to the nude figure before it was moved here. It now stands facing the point where the Sava joins the Danube.

You started among the museums and traffic of Republic Square and finished on a ridge above two rivers, which is how most of Belgrade's history actually unfolded: the city grew from the fortress outward. To return to the centre, walk back through Kalemegdan park, which has plenty of paths and benches.