In the fading light of a summer's day, I can hear her before I see her. Above the streak of the violins, her voice rises like a cry from the abyss, like the yearning of the earth. "Don't ask me where the love has gone, my heart," she is saying, "Pour me a drink and let us drink of its ruins." Now I start to see them through the trees, first in twos, straggling out of view, eyes and lips closed and open, open and closed, drinking each other's breath to the rhythm of the words. What does it say about the modern world that these lovers tingling to the words of Umm Kulthum, the singer of the Arabs, are not Egyptians or Moroccans, but Dutch? That the park is not Al-Azhar or Zabeel but Oosterpark, in the east of Amsterdam? The songs of Umm Kulthum, as sung by the Egyptian singer Amal Maher, opened this year's Holland Festival two weeks ago, packing out the Royal Theatre Carré and bringing thousands of people out for a picnic as it was beamed live to Oosterpark. If anything tells you what Amsterdam is today, it is the sight of thousands of Dutch men and women, old and young, clapping and dancing, taking their cues from the Arabs in their midst, these songs in their blood, who start their clapping and ululation a fraction of a second earlier. Indeed Amsterdam today is many things in one. It is Europe's greenest capital city, a small metropolis of barely two million people that gave rise to some of Europe's greatest art and architecture and a far-flung maritime empire. It is open and relaxed, yet also old-fashioned and reserved. And it is still tolerant, revelling in its liberality, despite the tensions the newspapers report, despite the political rewards the far-right has gained elsewhere in the country. Nothing quite encapsulates Amsterdam's sense of history and style as the bicycles treading its streets: the elegance and classic design of the bikes has become retro and funky. Amsterdammers love their bikes and live their lives on them. They flirt: here are a couple in Jordaan, giggling as they ride together. They conduct business: here are these two men in suits, riding bikes with briefcases behind Dam Square, one making a phone call. They even parent: in Frederiksplein, east of the centre, I see a young boy riding pillion behind his father. Next to him rides his mother, berating him, while he looks the other way, sulking at the people whizzing past. Without these wheels and without its water, Amsterdam would be a different city and both remain the best way to understand it. Either renting a canal bike, a small boat propelled by pedals, around the waterways, dipping under the arches of bridges, or taking a bike and rolling from Dam Square, the spiritual heart of the city, away from the dazed-looking tourists, across the canals that have made the city what it is, all the way down Leidsestraat to the Vondelpark, which swallows you with its little lakes and trees into a different Amsterdam.
Amsterdam, indeed, has many different faces. For most tourists, especially the young, it is a city of freedom, a place of smoky cafes and red lights, where the normal rules of home don't apply. But step outside the bubble of the centre bordered by the Singel river, and a completely different city unfolds. Go south - just a few minutes by bike, this being Amsterdam - and here is the Museum square, with the Rijksmuseum at its apex, and the Van Gogh and modern art Stedelijk museums around it. The country's flagship space, the Rijksmuseum, is being renovated but most of its best paintings from the Golden Age have been squeezed into the small Philips Wing. Here, art lovers coo at Falconet's statue of Cupid and crowd around Rembrandt's Night Watch. But it is the paintings of the Golden Age that bring the city to life, showing the people and the places that made the city what it is. The Golden Age was a period of around a hundred years from the late 15th century when the wealth, influence and population of Amsterdam exploded. From their small base on the lowlands of Europe, Dutch ships took off around the globe, trading and establishing key settlements on some of the most far-flung regions. They went west and established New Amsterdam on an island across the Atlantic: it later grew to become New York. In the south, they laid the foundations of what became Cape Town, in South Africa. And they went east, so far east as to return on themselves, taking the name of the Dutch region of Zeeland to the furthest limit of European colonialism, to two islands in the south Pacific. That trading instinct hasn't gone away - you can see it in the number of successful international businesses that were born or live in the city. You can see it in the opulent Oost-Indish Huis near Nieuwmarkt, the former headquarters of the Dutch East India company. You can see it in the markets around Waterlooplein, where antiques and bric-a-brac mix with colourful clothes and ageing DVDs. And you can see it in the celebrations of Queen's Day in April, when the city erupts in festivity and a tax dispensation means people bring their clothes and wares on to the streets to sell. Its legacy is clearest in the tree-lined avenues along the canal belt, the semi-circular girdle of waterways the Dutch call the Grachtengordel. This is where the traders of the city displayed their wealth, building tall, opulent, intricately-designed houses (but keeping them thin, as they were taxed on the width). The money that rolled in from the East and West India Companies ended up here, the revenues from trading coffee and tea, tobacco, spices and - less palatably - slaves. The expensive cars dotted around and the careful furnishings visible through the modern windows show the wealth is still there.
Even in decline, they trade. All along the waterfront, on the banks of the IJ channel, east and west from Centraal station, the buildings of the old harbour are being redeveloped, places that echoed to dockers now remixed to serve the brash youth. They come to places like Odessa, a replica of a Russian merchant ship that serves as a knowingly hip restaurant or go across the water to up-and-coming Amsterdam Nord, kicking off their shoes and singing in Tolhuistuin, a small garden hosting a series of mini weekend festivals of music and performance art all through the summer. But it is the area south of Centraal station that is best known, the medieval heart of the city. Alive with noise at any time of the day or night, it is an endless parade of backpacks and people, half-finished conversations and half-started friendships. In the mix of streets around Amsterdam's oldest church, the 14th century Oude Kerk, are glimpses of the city's history: the curious shops around Zeedijk, the heart of the Chinese community where street names are written in Mandarin; the quick and steamy packages of Asian food brought by Indonesian immigrants whose ancestors lived under Dutch rule; the young groups of teenagers speaking quickly in Dutch with a mix of Surinamese words - and linking it all are the souvenir shops and cafes that cater to the crowds of tourists.
In the middle of the day, with people, trams, bicycles and cars all sharing narrow streets, it can feel like an obstacle race. Within the canal belt the roads radiate, one merging into another, cutting across each other - high street shops here, music shops there. The roads lead inevitably to the large squares of Leidseplein and Rembrantsplein, full of outdoor cafes, theatres and restaurants, where Amsterdammers come to relax. Once past the canal belt, the noise fades. Bicycles regain the upper hand and everything slows down: the Dutch gliding peacefully along the city's bike lanes, as if nothing could disturb the tranquility of this trading city. The secret of their zen is in their stance: in contrast to the mountain bikes often seen elsewhere, which encourage cyclists to lean over the bike with their backs at a 45-degree angle, here the bikes push riders to sit back, their backs straight to the sky, giving them a peculiarly relaxed, open stance. I can tell you about these Amsterdams, because, for hours or days at a time, they were my versions of the city. But Amsterdam is a city to tune into, a place to find a space of your own. And for me, it came the first time I was a passenger on a bike. It was night, the last of my days in the city, and I was perched sideways on the back of a friend's bike, precariously zipping past canals with the bridges framed by light. There was a song playing and as I felt my time edging away, the singer captured my mood: "At last you can taste what you didn't know existed," she sang in Dutch, "But the clock is ticking. And everything goes round."