This is the walk of five hills, Capitoline to Palatine and between Caelian, Esquiline and Aventine. No steep gradients: except for the Janiculum across the Tiber, the hills of Rome are the gentlest of mounds.

Start: Begin on the Campidoglio, just south of Piazza Venezia and the grandiose marble monument, impressive in its snowy floridezza, to Victor Emmanuel the first King of united Italy (reigned 1860-78). Whatever you think of it as a work of architecture, it makes a magnificent landmark for the traveller in Rome.

The Campidoglio on Capitol Hill is the sacred hub of Rome. It challenges the Palatine as the city’s legendary nucleus. Here, traditionally, the she-wolf suckled the abandoned twins Romulus and Remus. The sculpture of the incident, familiar on coins, stamps and emblems of Italy, is right here in the Capitoline Museum (www.museicapitolini.org), along with other world-renowned works of antiquity including the Dying Gaul. The She-Wolf statue dates to 500 BC, but the thirsty twins were added later.

Myth and legend brood over this hill. Here and hereabouts was the Tarpeian rock (north-west side) where traitors were hurled to their deaths; the enclosure for the sacred geese, whose cackling saved Rome; the temple of trophies and of the Roman warriors’ spears, which waved of their own accord when danger threatened the city. A stairway of 122 steps rises to the 4thC church of Ara Coeli (‘Altar of Heaven’) on the Capitoline summit. On its site the Sibyl had earlier appeared to Emperor Augustus, predicting the birth of Christ. There are choice paintings in this church but its most revered treasure is an olivewood effigy of the Holy Child, said to have come from a tree in the Garden of Gethsemane, said also to have miraculous healing powers.

Michelangelo designed the Campidoglio we see today, the open piazza embedded in museums and palaces with graceful ramps and flights of steps leading up and down. The centrepiece is an equestrian statue of Emperor Marcus Aurelius in gilded bronze, wonderfully lifelike. Popular fancy has it that the horse is turning to gold and that, when the transformation is complete, he will sing to announce the end of the world. Descend from the Campidoglio gardens from the Campidogolio gardens on to Via dei Fori Imperiali, with the Forum on your right and behind it the Palatine Hill on which Romulus is said to have marked out the city limits when the city was a few caves and huts. Take the route slowly: it is all hallowed ground. The granite columns, arches and ruined temples of the Roman Forum are an evocation of pagan grandeur – thanks to Mussolini, who cleared all the slums in the 1930s and opened out the classical scene. Among at least 50 important monuments are the supposed tomb of Romulus; the Via Sacra and remains of the sanctuaries, which lined it; and a score of little temples, and basilicas over which the imagination runs wild. Observe that hole in the ground, for example, with a stone base and part of an arch across the way from it: that is the house of the Vestal Virgins and the hearth of the sacred flame that they tended. The girls, symbols of purity, were taken very young from patrician homes, kept in seclusion and trained in all the virtues. Once a year they had an airing in a closed chariot to a shuttered private box at the Colosseum. For misdemeanours such as letting their eyes wander they were flogged, sometimes starved to death. None the less Nature found a way and numerous pregnancies were recorded.

At the far end of the Forum relief maps in coloured stone put some flesh on the bones of the bare pillars and broken masonry, sunk below modern street level. On the right is the three faced Arch of Constantine; on the left Nero’s Golden House, whose ornamental waters the Colosseum eventually enclosed; in front, the Colosseum itself, like a 2,000-year-old multi-storey car-park. A cat population, tawny and well-fed with tourist titbits, basks on the tiers of this 50,000-seater stadium where, they say, gladiatorial combats did not normally take place; only mock sea fights and suchlike. (The place for the blood-and-thunder of a Roman holiday was the Circus Maximus, to which we shall come beyond the Palatine hill. It seated 385,000, two-thirds of ancient Rome’s population.) Note the secretive little alcoves round the Colosseum at ground level, handy for casual sex. Their name, fornices, put a word into modern languages.

Go straight-ahead now to San Giovanni in Laterano, cathedral and parish church of Rome, with a stern 17thC façade and the foundations of a 4thC chapel behind it. It is of this, not of St Peter’s, that the Pope is bishop and vicar. Pious visitors go behind this church to ascend on their knees the dim narrow Scala Santa (‘Holy Staircase’) of 28 marble steps encased in wood. Some believe that this was originally the staircase of Pontius Pilate’s house in Jerusalem.

Return to Piazza San Giovanni in Laterano and walk south beside Villa Celimontana and the Caelian Hill, to the Terme di Caracalla of AD 217, the largest of Roman baths. The popular al fresco summer opera has lately been suspended for fear of damage to the fabric.

Heading west on Via Terme di Caracalla you have the Aventine on the left, the Palatine on the right. If you feel energetic, explore the Farnesian garden, the site of Emperor Tiberius’s villa on the Palatine. Continuing west, the long rectangle of dry grass is the Circus Maximus and beyond it on Via Greca you come to Piazza Bocca della Verità and two delightful little pagan temples, also the church of Santa Maria in Cosmedin. In its porch you will find the ‘Mouth of Truth’: a Roman drain outlet in the form of a grotesque mask. Tell a lie with your hand in its mouth, says the legend, and you get it bitten off. (Last century the English traveller Augustus Hare actually saw someone bitten – by a scorpion nesting inside the mask.)

From the Bocca it is only a short step back by Via Teatro di Marcello to your starting-point on the Campidoglio. Gluttons for punishment can extend the walk 3 km by taking to the Tiber bank and walking upstream. Except in time of flood, or after spate when the walkway is muddy, you can stroll at the water’s edge, and there are steps to the riverside road at every bridge. Pass Ponte Fabricio and Ponte Garibaldi with the Tiber island, Isola Tiberina, and the landing stage for upriver excursion boats in between. Next is Ponte Sisto, the ancient Aurelian bridge with its occhialone or ‘big eye’ in the stonework, an old-time flood gauge.

Just off the Lungotevere (‘along the Tiber’ road) at this point stand two palaces. The Spada is now an art gallery. The Farnese, begun by Sangallo in 1515 and continued by Michelangelo, is elegant inside and out, generally reckoned Rome’s most beautiful building. Its lines may be familiar to you – many stately buildings including London’s Reform Club on Pall Mall have been modelled on it.

Across the Farnese piazza the Via Baullari takes you past the Baracco Museum (www.en.museobarracco.it)(Egyptian, Assyrian and Greek sculptures) to Piazza Navona, a great Roman rendezvous on account of its three huge and intricate fountain groups. On Bernini’s Four Rivers fountain the Nile hides her eyes – her source was unknown in 1601. Elaborate and proportionately costly ice-creams are served at piazza cafés, notably the Tre Scalini. At the south end of Piazza Navona try to find time for Palazzo Braschi: the museum of Rome (www.museodiroma.it). This place is full of curiosities, including the highly decorative but never-used coaches of the papal railway train. From an upper window you have a stirring view of the piazza and the three great fountains in line.

Now walk east to Piazza della Rotonda and the Pantheon of Rome, built 27 BC, enlarged 150 years later by Emperor Hadrian. Great size and noble proportions are its features. Raphael is buried here and so are the kings of reunited Italy. Take Via del Gesù, Piazza del Gesù and Via Aracoeli to return in 10 minutes to the Campidoglio.