Trajan's Market site features

Trajan's Market is a hillside of vaulted brick rooms stacked in tiers, and you climb it rather than walk round it. The structure is cut into the slope of the Quirinal in a great curve, storey above storey, so the route goes up through levels and comes out on terraces looking over the Imperial Fora.

It was probably built between 100 and 110 AD, by Trajan's own architect. Apollodorus of Damascus — who, as the record has it, always followed Trajan on his campaigns — is credited with it, and the ambition shows in the engineering rather than the ornament: the hemicycle holds back the hill as much as it houses anything.

The rooms themselves are plain, repetitive and barrel-vaulted. Rank after rank of them open off corridors and stairs, all in brick-faced concrete, with the vaults springing low and the openings arched. The repetition is the architecture; there is almost no decoration to look at.

Much of what you climb through is not Roman at all, and this is the thing to know. During the Middle Ages the complex was transformed by adding floor levels, still visible today, along with defensive elements including the Torre delle Milizie — the big square tower that dominates the skyline here and is the single most recognisable thing on the site. So an upper storey may be a thousand years younger than the one beneath it.

Later still it was a convent, then a barracks. A convent built in this area in the sixteenth century was acquired by the state in 1885 and became the Goffredo Mameli barracks, afterwards demolished — which is why the ancient fabric is exposed at all.

Inside, it works as a museum, and the exhibits come from elsewhere. The Museum of the Imperial Fora opened in 2007 and houses a wealth of artefacts from all of ancient Rome's fora, so the vaulted rooms hold marble that was never theirs — fragments of entablature, inscriptions and sculpture displayed at the height they would originally have been seen.

The terraces are the reward. From the upper levels you look straight down the length of the Imperial Fora, which is the view that makes sense of how the whole district was planned.

It is open longer than most Roman sites: every day, 9.30 to 19.30, with last admission an hour before closing, at Via Quattro Novembre 94.

The great hemicycle

The curved multi-storey facade that follows the line of Trajan's Forum. The single most recognisable thing here, and best understood from the terrace above rather than from the street below.

The Torre delle Milizie

The "militia tower", built into the complex in 1300. It is the medieval silhouette on the skyline above the Roman brick, and the physical evidence that the site was defended rather than quarried.

The Museum of the Imperial Fora

Opened in 2007 and holding material from all of ancient Rome's forums. It is the only place the whole sequence of imperial forums is presented together, which makes it the right stop before or after walking the Via dei Fori Imperiali.

The upper terrace

Looks down over the Forum of Trajan and across to the Vittoriano. The best vantage point in the complex, and the reason to go up before working down.

The medieval floors

Levels inserted during the Middle Ages and never removed. Several rooms are therefore Roman spaces at a height the Romans did not use — worth noticing rather than walking past.