For most of the eighteenth century, Lisbon's great public project wasn't a palace — it was getting clean water across a valley. The Aqueduto das Águas Livres did it with thirty-five arches that survived the 1755 earthquake intact, and it still strides across the Alcântara valley as if the city were built around it. This is the walk along its length, ending in the room where the water arrived.
Start at Campolide, where the arches step off the high ground, and work along the valley side to where the aqueduto (aqueduct) stands at full height — the central arch sixty-five metres up, the whole run nearly a kilometre. The walkway across the top has been shut since the 1850s, so this is a look-from-below walk; find the spot where the arches cut clean across the sky and stay there a minute.
Then climb east, following the arches as they lower into the city and vanish underground, to the Mãe d'Água das Amoreiras — a cistern the size of a small church, the water still black and silent inside, a roof terrace on top. End in the Jardim das Amoreiras under the mulberry trees, Rato and the metro five minutes down.

