Walk into the amphitheatre, one of the largest in the Roman empire, and find the pit under the arena floor

Walk the grid of Hadrian's new quarter and look at the mosaics still in the houses

Work out what came out of this town: Trajan, Hadrian, and the emperor Arcadius

Find out what happened in 1740, when Seville demolished the amphitheatre walls for building material

Work out why the site survives — the Hadrianic extension was abandoned while the old town kept going under modern Santiponce

Scipio Africanus settled his wounded soldiers in an existing Turdetanian town on the Aljarafe in 206 BC at the end of the Second Punic War in Hispania, and the place that grew from it produced Trajan and Hadrian — and Arcadius, Theodosius's elder son. Hadrian gave his birthplace an enormous new quarter with one of the largest amphitheatres in the Roman world. The town was never entirely abandoned, but the Hadrianic extension was, which is why it can be excavated at all. Seville pulled down the amphitheatre walls in 1740 to build a dyke on the Guadalquivir.

Itálica: The Town That Produced Two Emperors

Visit the Museo del Baile Flamenco in Seville's Santa Cruz quarter, founded by the dancer Cristina Hoyos

Watch a live flamenco show in Triana, the Seville quarter with the deepest flamenco tradition

Catch the Bienal de Flamenco, Seville's biennial festival held in September of even-numbered years

Flamenco came out of Andalusia from Romani, Moorish, Jewish and Andalusian roots, and it is not primarily a dance — the cante, the singing, is the core of it, and the good stuff is closer to grief than to entertainment. Triana in Seville, across the river, is the quarter with the deepest tradition. Tablaos for tourists exist and are fine; what you are hoping for is a night where the performers stop performing and something else happens, which cannot be booked and occasionally does.

Seville: Flamenco in Triana

Go down into the necropolis and find the Tomb of Servilia and the Tomb of the Elephant

Work out how a tomb cut down into rock was actually used, and by how many generations of one family

Go through the Puerta de Sevilla, which still has Carthaginian fabric in it and was later fortified as its own small alcázar

Work out what Carmona was under Islam: the capital of its own taifa kingdom

Climb to the Alcázar del Rey Don Pedro for the view over the Seville plain

Carmona stands on a ridge over the Seville plain and has been fortified since the Carthaginians. Its Roman necropolis, of around the 1st century, is the thing to come for: family tombs cut down into the rock, with the Tomb of Servilia and the Tomb of the Elephant the two to find. The Puerta de Sevilla keeps parts of its Carthaginian phase and was later fortified as a small alcázar in its own right; the walls the Romans built were reused and modified by everyone who came after. Carmona was the capital of one of the taifa kingdoms in the Islamic period, and the Alcázar del Rey Don Pedro above the town is now a parador.

Carmona: A Roman Necropolis and a Moorish Gate

Take a guided 4x4 safari through Doñana National Park, the 543km² reserve UNESCO listed as a World Heritage Site in 1994

Walk the trails and bird observatories from the El Acebuche visitor centre

Look for the Iberian lynx and the Spanish imperial eagle among the park's more than 300 bird species

Visit El Rocío, the village that draws about a million pilgrims to its annual pilgrimage

Doñana is where the Guadalquivir meets the Atlantic — 543 square kilometres of marsh, shifting dunes and pine and cork woodland, and the most important wetland in Europe for migrating birds, sitting on the route between Europe and Africa beside the Strait of Gibraltar, with over 300 species recorded annually and up to 200,000 waterfowl wintering in the marshes. It is also a stronghold of the Iberian lynx and the Spanish imperial eagle, both of which came very close to disappearing. The park is under constant pressure from aquifer extraction for strawberry farming, which is the fight that decides whether it survives.

Doñana: The Marshes Between Europe and Africa

Stand at the water and look at a river with a pH of under 3 that is full of life

Work out what lives in it — acidophile organisms that eat minerals, some of them endemic to this river

Find out why NASA studies this valley and what it has to do with Mars

Look into Corta Atalaya, at one time the largest open-cast mine in Europe

Ride the restored Riotinto mining railway, built by the Rio Tinto Company Limited to get ore to Huelva

Find the English quarter the British company built for its managers and engineers from 1873 onwards

The Tinto runs deep red with a pH between 1.7 and 2.7 and a heavy load of iron, copper, cadmium and manganese — the product of weathering pyrite and chalcopyrite in the ore bodies along it. Nothing should live in that, and yet it is full of acidophile micro-organisms, prokaryote and eukaryote both, including fungi and algae endemic to the river, which feed on minerals alone. NASA picked it as a habitat to study for its possible resemblance to conditions on Mars. Above it sits Corta Atalaya, once the largest open-cast mine in Europe.

Río Tinto: The River NASA Studies to Understand Mars

Walk the wall circuit — about two kilometres of rammed earth and brick with fifty towers

Find the five gates and work out which is Roman and which Muslim work

Work out what the taifa of Niebla was: independent from 1234, reaching to Cape St Vincent, and still holding out after Córdoba and Seville had gone

Cross the old bridge over the Tinto and look at the colour of the water coming down from the mines

Go into the church of Santa María de la Granada, which was a mosque and before that a Visigothic church

Niebla has about two kilometres of almost complete wall in rammed earth and brick, with fifty towers and five gates, wrapped round a small town above the Tinto — the same red river that comes down from the mines. It was capital of a cora under the caliphate and then of the taifa of Niebla, which in 1234 recovered its independence under Abenmahfot and ran from the mouth of the Guadalquivir to Cape St Vincent, taking in much of what is now the Algarve — and held out against Castile for decades after Córdoba and Seville had fallen. Alfonso X finally took it in 1262 after a nine-month siege.

Niebla: Roman, Muslim and Still Walled

Go into San Juan Bautista and find the Zurbaráns, still hanging where they were made to hang

Walk through the Arco de la Rosa and work out what it was part of

Find out what happened in 1368 when Muhammad V sacked the town and knocked the walls down

Walk the Plaza Ducal and the remains of the alcazaba turned seigneurial castle

Work out who the Ponce de León were and what the house of Arcos became

Ferdinand IV granted Marchena in 1309 to Fernando Ponce de León, and the family held it for centuries as the lordship from which the house of Arcos descends. In 1368 Muhammad V of Granada, allied to Peter I of Castile, sacked the town and pulled down its walls; the 14th and 15th centuries rebuilt them and turned the old alcazaba into a proper seigneurial castle. The church of San Juan Bautista holds a set of Zurbarán paintings still in the building they were painted for, and the Arco de la Rosa is the surviving gate of the walled enclosure.

Marchena: The Dukes of Arcos and a Room of Zurbaráns

Go into Menga and sight down the corridor at the Peña de los Enamorados, which is what it points at

Work out how unusual that is: 99.99% of Mediterranean dolmens are oriented on the sky, and this one is not

Go into the Viera dolmen next door, which is oriented on equinox sunrise like everything else

Go to the tholos of El Romeral and work out its double alignment — the Torcal, and the winter solstice midday sun

Find the intermediate pillars inside Menga, a solution used nowhere else, holding up capstones at the limit of what the type could carry

Michael Hoskin found that 99.99% of dolmens around the Mediterranean are oriented on the sky — usually sunrise at the equinoxes, as the Viera dolmen here is. Menga is not. Menga is aligned on the anthropomorphic profile of the Peña de los Enamorados, and specifically on the Matacabras shelter on it, where there is rock painting. El Romeral is aligned on the Torcal, where the Cueva del Toro is, and on the midday sun at the winter solstice. UNESCO listed all four elements — two dolmens, a tholos and two mountains — in 2016.

The Antequera Dolmens: Megaliths Aligned on a Mountain

Walk down the terraces and work out that the whole city is built on three levels with the caliph at the top

Go into the Salón Rico and look at what has been pieced back together from the rubble

Work out the timeline: begun 936, destroyed 1010 to 1013, standing for under eighty years

Find out why it was built at all — a new caliph needing to outshine the Fatimids in North Africa

Go to the museum first, which is underground and explains the site before you see it

Abd al-Rahman III declared himself caliph and then did what a caliph was expected to do: founded a new city to prove it. Medina Azahara went up from 936 to 940 and on through his reign and his son al-Hakam II's, eight kilometres outside Córdoba at the foot of the Sierra Morena, explicitly to outshine the Fatimid caliphate in North Africa. Then Almanzor moved the administration to his own new city, and in the civil war of al-Andalus Medina Azahara was destroyed between 1010 and 1013 and quarried for its stone. UNESCO listed it on 1 July 2018.