Climb Pica d'Estats, at 3,143m the highest mountain in Catalonia, on the Spain–France border above the municipality of Alins; Henry Russell and Jean-Jacques Denjean made the first ascent in 1864

Stand on the neighbouring summits of the massif, Pic de Verdaguer (3,131m) and Punta Gabarró (3,115m)

Walk in the Alt Pirineu Natural Park, Catalonia's largest natural park at 69,850 hectares, created in 2003

Look for the Pyrenean chamois on the high slopes

Pica d'Estats is 3,143 metres and the highest point in Catalonia, standing right on the French border in the Pallars Sobirà — Henry Russell and Jean-Jacques Denjean made the first ascent in 1864, and Russell went on to become the great obsessive of the Pyrenees, eventually leasing a mountain. It is a long day from the valley with over 1,800 metres of ascent. Around it is the Alt Pirineu Natural Park, at 69,850 hectares the largest in Catalonia, created in 2003 and holding chamois, bearded vulture and a very small number of brown bears.

Pica d'Estats: The Roof of Catalonia

Walk up from the first hairpin of the D 8 above Aulus-les-Bains, on the road toward the col de Latrape, taking the forest track between wood and pasture, crossing the passerelle de l'Artigou at 1,060 m and following the right bank of the Arse to the foot of the falls at 1,380 m — about 90 minutes each way

At the foot of the falls, trace the water down through all three stages: the single 100 m drop at the top, the head of hair of small cascades below it, and the point where they gather back into one last fall

In the thermal park at Aulus-les-Bains, find the grotto built in 1873 to house the springs that the Romans knew but which only made the village's name in the 1820s, and the war memorial of 1924 in front of the pont du Midi

At Aulus-les-Bains find where the Arse, which rises at the foot of the pic de Turguilla on the Spanish border and carries the falls at its midpoint, empties into the Garbet

From the spa village of Aulus-les-Bains, in the Pyrénées ariégeoises regional park, a path climbs about 90 minutes to the Cascade d'Ars at 1,380 m in the Garbet valley: 246 m in all, a single drop of 100 m breaking into a fan of small falls that regroup into one last cascade. Fr.wikipedia calls it one of the most picturesque and imposing in the Pyrenees, and the 19th-century pyreneist Count Henry Russell put it ahead of every rival. The falls and their valley have been a classified site since 11 October 2018.

Aulus-les-Bains and the Cascade d'Ars: The 246m Falls of the Couserans

Start up the Riberot valley from the Pla de la Lau car park at Bordes-Uchentein, the one standard way in, and follow it towards the col de Faustin on the south side

Sleep at the refuge des Estagnous at 2,246 m, and if you have the gear and the head for a route graded D, take the via ferrata built in 2000 between the refuge and the étang Long — 1,200 m of it, 620 m equipped, hanging over the étang Rond

Reach the 2,839 m summit and find the cross standing there now, inaugurated in September 2012 after the granite one of 1987 was smashed by vandals in 2011 — the latest of a line that is said to start with the bishop Valerius and includes the marble cross Bernard Coignet de Marmiesse raised in the 1670s

Walk a stretch of the Chemin de la Liberté where it crosses the Valier massif, and from high ground pick out the line it takes from Saint-Girons towards the col de la Pale de la Clauère and over into Catalonia at Esterri d'Àneu — the way 782 people got out between 1940 and 1944

From the summit ridge look down the north-east flank onto the glacier d'Arcouzan, the most easterly glacier left in the Pyrenees — about 2.8 hectares in 2013, lying between 2,350 and 2,500 m

Mont Valier stands 2,839m over the Couserans in the Ariège and takes its name from Valerius, the legendary first bishop of Couserans, who the story says climbed it in the 5th century; a later bishop had a marble cross put up there in the 1670s. These same mountains carried the Chemin de la Liberté, the escape route named in 1994, over which 782 people got out to Spain between 1940 and 1944.

Mont Valier: The Ariège Summit and the Freedom Trail

Go into the cathedral, the only entirely Romanesque one left in Catalonia, and find the open gallery across the apse

Work out that the bishop of this town is a co-prince of Andorra and what that actually means

Drive or walk to a viewpoint on the Cadí wall and look along twenty kilometres of unbroken limestone

Find the Pedraforca and work out why a mountain with two prongs got that name

Look for chamois on the Cadí, which holds one of the densest populations in the Pyrenees

La Seu d'Urgell sits where the Valira meets the Segre below Andorra, and its bishop is still one of the two co-princes of Andorra — a head of state living in a Catalan market town. Its 12th-century cathedral is the only entirely Romanesque cathedral left in Catalonia and is unique there for how Italian it looks — a contract of 1175 gave one Ramon Llambard seven years to close the vaults and raise the towers, and he was probably Lombard, which is where the style came from. The church was never finished. East of the town the Cadí-Moixeró natural park runs along a limestone wall over twenty kilometres long, with the Pedraforca — a mountain split into two prongs — as its landmark, and one of the strongest chamois populations in the Pyrenees.

La Seu d'Urgell and the Cadí

Walk out to the Estany de Sant Maurici and look across at Els Encantats, which is the park's logo

Find the meanders of the Sant Nicolau between Llong and Llebreta, which are what the park is named after

Work out how the meanders formed: a lake silted up flat and the river had nowhere to fall

Do a lake-to-lake day on the Carros de Foc refuge circuit, or a section of it

Work out that this is the only national park in Catalonia and why that is

Aigüestortes i Estany de Sant Maurici was created in 1955 and is the only national park in Catalonia — high Pyrenean granite scattered with almost two hundred lakes of Quaternary glacial origin. Between the Llong and Llebreta lakes the Sant Nicolau river runs in tight meanders across a flat where an old lake silted up, and those meanders — aigües tortes, twisted waters — give the park its name. The view across the Estany de Sant Maurici to the twin peaks of Els Encantats is the park's own logo.

Aigüestortes: Catalonia's Only National Park

Raft or kayak a stretch of the Noguera Pallaresa from Sort

Walk up to the castle of the Counts of Pallars at the top of the town

Walk the old centre between the castle and the parish church, the former walled town

Sort is the capital of the Pallars Sobirà, strung along the Noguera Pallaresa, a river that rises beside the Garonne on the Pla de Beret and runs its whole course through the province of Lleida. In its upper reaches it is known for white water that is rafted and kayaked, and it runs straight through Sort. Above the old walled centre stands the castle of the Counts of Pallars, documented from the 13th century, though the town was tied to the counts from the 10th. The name looks like the Catalan word for luck, but it is older than that and probably means a bridge — the one important crossing of the river.

Sort: White Water on the Noguera Pallaresa

Soak your feet in the Bassin des Ladres in the middle of Ax-les-Thermes — the town's only listed monument — and work out how the water gets cool enough to sit in: it leaves the ground at up to 77 °C, the hottest in the Pyrenees, and has to lose forty degrees on the way to your ankles

At the Maison des Loups, pick out all five packs — Arctic, Canadian, European, Polish and Mackenzie — and rank them by size on the hoof rather than by label, then book a place in the vision tunnel at the till and see how close the Mackenzies come to the glass

Walk up the Oriège from Les Forges d'Orlu at 912 m towards the étangs d'En Beys at 1,950 m and look for two of the reserve's residents: the isard on the rock above the path, and the Alpine marmots that were put here in 1958. Then remember what the reserve has logged coming back on its own — a bearded vulture nesting site in 1997, red deer in 1998, a brown bear in 1999 and a grey wolf in 2001, a few kilometres above a park built to show people what a wolf is

On the way up the Oriège, find the hydroelectric works inside the reserve: the intakes at Mourtès and la Coumette and the dam at En Beys are all within its boundary, and the flow left in the river below them is set by law rather than by the weather

At Ax-les-Thermes the sodium-sulphide springs run at up to 77 °C, the hottest in the Pyrenees, and were already known in Gallo-Roman times. In 1260, on Saint Louis's order, count Roger IV built a leper house beside the Bassin des Ladres to treat crusaders who had come back from the Holy Land with leprosy; the basin is the town's one listed monument, inscribed in 1979. Up the Oriège at Les Forges d'Orlu, the Maison des Loups keeps packs of Arctic, Canadian, European, Polish and Mackenzie wolves, and above it the national wildlife reserve of Orlu covers about 4,250 hectares between 950 and 2,765 m, climbing past the dam to the étangs d'En Beys at 1,950 m.

Ax-les-Thermes and Orlu: The Lepers' Pool, the Wolf House and the Reserve under the Frontier Peaks

Stand in the trading hall of the Llotja among its eight twisted columns, eleven metres high — meant as palm trunks holding up a sky once painted blue with gold stars

Look for the carved gargoyles on the outside of the Llotja

Shop in the Mercado Central, the modernista market finished in 1928

See the Holy Chalice in its chapel in Valencia Cathedral, given by Alfonso the Magnanimous in 1437

The Silk Exchange in Valencia, the Llotja, was designed by Francesc Baldomar around 1470 and finished after his death by Pere Compte and Joan Ivarra, on the model of the exchange in Palma: a great hall of twisted columns holding up Gothic vaults, built to house the maritime trade court and to show off the city's 15th-century wealth. It has been a UNESCO World Heritage Site since 1996. Across the square the Mercado Central, begun in 1914 and finished in January 1928, is one of the masterpieces of Valencian modernisme and still a working food market. A few streets away, in a side chapel of the cathedral that was once its chapter house, is the Holy Chalice, dated to the 1st century and given to the cathedral by King Alfonso the Magnanimous in 1437.

Valencia: The Silk Exchange, the Central Market and the Holy Chalice

Walk the Vila Vella of Tossa de Mar, the only fortified medieval town still standing on the Catalan coast, with its 12th-century walls, four turrets and three cylindrical towers of the 14th century

Visit the Tossa Municipal Museum, with its work by Marc Chagall and the mosaics from the 1st-century Roman villa of Els Ametllers

Walk a stage of the Camí de Ronda, the coastal path along the 214km Costa Brava between Blanes and the French border, around Tossa's coves

Tossa de Mar has the only fortified medieval town still standing on the whole Catalan coast — 12th-century walls with three cylindrical towers running down to the sea, enclosing a knot of lanes on a headland. The Costa Brava got its reputation in the 1960s and has spent decades living it down, but the 214 kilometres between Blanes and the French border are genuinely rugged, and the Camí de Ronda that runs along them was a coastguard and smugglers' path long before it was a walking route. Marc Chagall came here in the 1930s and called it a blue paradise.