Walk beside the Roman Aqueduct, built of about 25,000 granite blocks fitted without mortar, spanning 818m with over 170 arches and reaching 29m

Tour the Alcázar, a fortress documented for the first time in 1122 that became a favoured royal residence

Enter the Cathedral, built between 1525 and 1577 and one of the last Gothic cathedrals in Europe

Eat cochinillo asado, roast suckling pig, at a mesón beside the aqueduct such as Mesón de Cándido

The aqueduct at Segovia is about 25,000 granite blocks held together by nothing at all — no mortar, no clamps, just the weight and the cut of the stone — carrying water 818 metres across the town on over 170 arches, up to 29 metres high. It was built in the 1st or 2nd century AD and it carried water until the 1970s. Above it the Alcázar sits on a rock where two rivers meet, first documented in 1122, and the cathedral of 1525–1577 is one of the last Gothic cathedrals built anywhere in Europe.

Segovia: The Aqueduct, the Alcázar and a Late Gothic Cathedral

Be there when the fountains run and work out that all twenty-one are driven by slope alone, with some jets clearing forty metres

Find El Mar, the 216,000 cubic metre reservoir at the top of the garden that feeds the whole system

Work out the contradiction: a Spanish king raised at Versailles who said he wanted another Escorial and built this instead

Find out why the palace is irregular — the 1719 order that nothing already standing was to come down — and why the fountain statues are lead rather than bronze

Go to the Real Fábrica de Cristales in the village, the royal glass works that supplied the palace

Philip V was born at Versailles in 1683 and raised at the court of his grandfather Louis XIV, and when he came to build himself a retreat below the Guadarrama it showed. He ordered a chapel here in 1719 with the instruction that nothing old was to be demolished, which is why the result is irregular and reads as a set of additions. The main works began in 1721. The gardens were laid out by the French gardener René Carlier, who used the natural slope of the surrounding hills both for the perspective and as the power source for all twenty-one monumental fountains; Carlier died in 1722 and Étienne Boutelou continued the work. Where Versailles struggled for water pressure, La Granja simply fell downhill — and some of its jets clear forty metres.

La Granja de San Ildefonso: Versailles on the Meseta

Hike from the Puerto de Cotos to the summit of Peñalara at 2,428m, the highest peak of the Sierra de Guadarrama

Look down on the glacial lake and cirques beneath Peñalara, protected as the Peñalara Natural Park in 1990 and now part of the Sierra de Guadarrama National Park, declared on 26 June 2013

Visit the Peñalara visitor centre at the Puerto de Cotos, the start of the summit path

Peñalara is the highest point of the Sierra de Guadarrama at 2,428 metres, an hour from Madrid, and the corries beneath it hold the southernmost glacial lakes in Europe of their kind — cut by ice that has been gone for ten thousand years. It was protected as a natural park in 1990 and folded into the Sierra de Guadarrama National Park when that was declared on 26 June 2013. The path from Cotos is short and popular, which is why numbers to the summit are now limited at busy times.

Peñalara and the Glacial Cirques

Go into the church and find the grille made by the Carthusian monk Francisco de Salamanca

Find the walnut choir stalls carved in the 16th century, removed to Madrid in 1883 and returned here in 2003

Work out the founding story: a king who burned a charterhouse in France and built this one in 1390 to make up for it

Walk the Lozoya valley around it, which is inside the Sierra de Guadarrama National Park

Cross to the Puente del Perdón and find out what it was called that for

Henry II of Castile ordered a charterhouse built in the Lozoya valley in 1390 — the first Carthusian foundation in Castile — and tradition says he chose that order because his own army had burned one of their houses during the war in France. He picked the spot himself, beside a hermitage already there, and told his son, the future John I, exactly where. It was Carthusian until 1835. The grille separating the congregation from the monks was made by a Carthusian monk, Francisco de Salamanca, and the 16th-century walnut choir stalls were taken to Madrid in 1883 and only brought back in 2003.

El Paular: The First Carthusian House in Castile

Walk the paved sections up towards the Fuenfría pass through the pine forest

Find the bridges — Enmedio, Descalzo, La Venta and Reajo — proposed for protection in 1981

Work out the argument: the visible track is not the 1st-century road along its whole length

Find out what the Cercedilla milestone of 1910 settled and what it did not

Cross the pass and look down into the Valsaín valley on the Segovia side

A Roman road crossed the Guadarrama here, linking Segovia with Miaccum and on to Toledo, over the Fuenfría pass between the Fuenfría and Valsaín valleys. A milestone turned up at Cercedilla in 1910 and let the archaeologist Antonio Blázquez date the crossing securely, though his reconstruction of the line has been argued over ever since — later work by Rivas López, Rodríguez Morales and Moreno Gallo showed the present paved track does not follow the 1st-century road everywhere. The road and its four bridges were put forward for protection on 2 July 1981.

The Fuenfría: A Roman Road Over the Guadarrama

Walk the upper gallery and work out that this is a palace wearing a castle's clothes

Find the Romanesque-Mudéjar church swallowed inside the structure when the castle was built over it

Work out Juan Guas's Isabelline Gothic and its Hispano-Muslim borrowings, and what he did next at Guadalajara

Find the remains of the old castle nearby, which this one replaced

Walk up into La Pedriza behind it, the granite massif the family's land ran into

The Mendoza were one of the most powerful families in late medieval Castile, and in the last third of the 15th century they replaced their old fortress at Manzanares with something grander — a palace-fortress built over a Romanesque-Mudéjar church, which was simply absorbed into the structure. Juan Guas drew it in Isabelline Gothic with Hispano-Muslim influence, and it is regarded as the precursor of his Palacio del Infantado at Guadalajara, where he settled the template for a Catholic Monarchs palace. It stands under the Guadarrama beside the Santillana reservoir, with La Pedriza behind it.

Manzanares el Real: A Castle Built to Be Lived In

Go in through the single gate and work out that there is no other way in or out of the village

Find the prison in the gate tower, and find out why the jailer held the keys to the village at night

Find the arms of Íñigo Fernández de Velasco over the entrance, from the 16th-century rebuilding

Come on one of the July candle nights, when the village kills every electric light for a concert

Walk to the castle at the far end, which Ignacio Zuloaga bought and used as a studio

Pedraza has one way in and out. The gate goes back to the 11th century and was rebuilt in the 16th under Íñigo Fernández de Velasco, whose arms are over the entrance; its black poplar doors were shut every night for centuries, and if anyone needed to pass after dark it was the jailer's job to open them, because the village prison is in the gate tower. The whole place was made a Historic Ensemble in 1951 and has about three hundred and thirty-five inhabitants. On two Saturday nights in July it turns off every electric light and holds a concert by candle.

Pedraza: A Walled Village With One Gate

Walk round the upper lagoons — the Gitana, the Tejo and the little Tejo — and name the colour of each

Look down into the lagoons from the rim and work out how a collapsed sinkhole fills with groundwater

Walk among the Torcas de los Palancares, the dry sinkholes of the same geology

The lagoons of Cañada del Hoyo are seven karst lakes — five lagoons and two smaller lagunillos — in the Palancares hills 40 kilometres from Cuenca, fed from underground and by rain, and a Natural Monument since 2007. Each looks a different colour because of microorganisms, submerged plants, the light and the season, though a glass of water from any of them is clear: the Tejo is dark blue, the little Tejo black, Cardenillas sky blue, the Parra blue. The Gitana was blue too, and has been green since the 1980s from the number of people bathing in it. Their levels drop a little every year as the aquifer is pumped. Eight kilometres away the Torcas de los Palancares are the same sinkholes without the water.