Walk the wall — 11th-century Moorish work restored in the 15th, and one of very few surviving circuits in the Madrid region

Work out how the defence works: the wall on one side, the Lozoya wrapped round the other three

Go into the Picasso museum and work out how a small town on the Lozoya came to hold a collection like it

Find out who Eugenio Arias was — a barber from Buitrago, and a friend of Picasso

Go into the 15th-century Gothic-Mudéjar castle and the church of Santa María del Castillo of 1321 beside it

Buitrago is one of very few towns in the Madrid region to have kept its walls — Moorish, 11th century, restored in the 15th — on a peninsula with the Lozoya running round it. Inside is a Gothic-Mudéjar castle of the 15th century, the church of Santa María del Castillo of 1321 in the same style, and, unexpectedly, a Picasso museum. Eugenio Arias was a barber from this town and a friend of the artist, and the collection he built is now held here.

Buitrago del Lozoya: Walls and a Picasso Collection

Book and walk the free guided visit through the beech wood

Find the map in the reception hut that shows where the other beech woods lie, and why this one is not the most southerly

Look for where the wood meets the Jarama on the border with Guadalajara

The Hayedo de Montejo is 250 hectares of beech forest on the slopes of the Sierra de Ayllón, on the Jarama at the northern tip of the Madrid region. Beech belongs in central Europe, and it survives here from the end of the last Ice Age because the hillside stays in shade and catches the moisture from the air. It was declared a Natural Site of National Interest in 1974 and in 2017 joined UNESCO's Primeval Beech Forests of the Carpathians and Other Regions of Europe. Visits are free, guided and limited. It is often called the most southerly beech wood in Europe; it is not even the most southerly in Spain, and the guides explain why.

The Hayedo de Montejo: A Beech Wood Left Over From the Ice Age

Walk the upper village and work out that the walls and the roofs are the same material — black slate, all of it

Find out about the Reyes de Patones, hereditary kings of a village of seven households, who lasted until about 1750

Work out when and how the kingdom ended: a request for a mayor, and independence from Uceda in 1769

Walk the hillside above, low rocky scrub of rockrose and broom with pine on the north face

Go down to Patones de Abajo, where everyone actually lives now, and see the difference

Patones de Arriba had seven households in 1555 and, by long tradition, its own hereditary kings — the Reyes de Patones — who lasted until about 1750, when the villagers asked to have a mayor instead. In 1769 Patones was granted the status of a village independent of Uceda, which is probably when the last king disappeared. It is the best example of arquitectura negra in the Madrid region: everything, walls and roofs both, built of black slate, on a rocky scrub hillside an hour from the capital.

Patones de Arriba: The Village With Its Own Kings

Find out who Cisneros was and how far one man from this town reached

Go into the church of Santa María Magdalena and work out why a town this size has one that size

Walk the surviving stretches of the town wall

Find the Canal de Isabel II works and work out what Madrid drank before it was built

Go up into the Sierra Norte behind, which is the emptiest corner of the Madrid region

Cardinal Cisneros — regent of Castile, founder of the university at Alcalá and the man behind the Complutensian Polyglot Bible — was born in Torrelaguna in 1436, and the town he came from is a compact walled place at the foot of the Sierra Norte with a church out of all proportion to it. It is also where the Canal de Isabel II starts: the 19th-century engineering that finally gave Madrid a reliable water supply, taking the Lozoya and carrying it seventy kilometres to the city, which is the single change that made the modern capital possible.

Torrelaguna: Cisneros and the Canal

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

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

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

Walk the planned centre and work out that the palace, church and workshops were designed as one building

Find out who Churriguera was and why the family name became a word for a whole style

Work out what was made here: a glass factory founded from nothing, with a town built round it between 1709 and 1713

Work out why the church is dedicated to Francis Xavier, and what that says about where the founder came from

Work out where Goyeneche came from and why the town is named after a Navarrese valley

Juan de Goyeneche was a Navarrese businessman from the Baztán valley who, at the beginning of the 18th century, decided to build an industrial town from nothing east of Madrid — a palace, a church and workers' housing on an orthogonal grid, designed as one scheme by José Benito de Churriguera between 1709 and 1713. It was built around a glass factory Goyeneche founded from nothing, and Spanish urbanists including Fernando Chueca Goitia have called the layout a model of native Baroque town planning. The palace and its church, dedicated to the Navarrese saint Francis Xavier, have been protected as a cultural asset since 16 March 2000.

Nuevo Baztán: A Baroque Company Town

Go into the basilica and work out that every metre of it is cut into the rock

Work out who built it: Republican political prisoners, between 1940 and 1958

Find out how many are buried here, from which sides, and why they cannot now be separated

Find out what was moved out in 2019 and in 2023, and what the 2022 renaming was for

Decide for yourself what a country should do with a monument like this, which is the live argument in Spain

Franco ordered this built in 1940 and it went up between 1940 and 1958, largely with the labour of Republican political prisoners. A basilica entirely underground, an abbey, and a cross 150 metres high on the crag above. Shortly before it opened in 1959 the remains of Republican soldiers were brought in, so 33,847 dead from both sides lie here, mixed together — the largest mass grave in Spain, and the bodies are now so far into the fabric that exhumation is considered impossible. Franco's own remains were moved out in 2019 and José Antonio Primo de Rivera's in 2023. It was officially renamed the Valle de Cuelgamuros in 2022.