AMSTERDAM is defined by its canals. Built 400 years ago in concentric horseshoes, they are the rib cage of the city. Coasting their waters on a canal boat opens windows onto a history of vast wealth and global power. The cobbled streets alongside the canals are scenic urban pathways for walking or biking. And they are anchors for funky shops, and cafes. The inner city of the Dutch capital is a compact warren of heritage buildings, of museums both grand and odd, of hidden gardens and outdoor markets — all within easy reach by any mode of transport except the unwelcome car. No longer the bargain city of Europe, Amsterdam is still a town of wonders that can be had for a discount, and sometimes for free. Walking and biking Seeing 17th century Amsterdam, with its proud past and sometimes quirky culture on display, from a bike or on foot is a happy cost-free experience. Among its 2,000 or so bridges, the Bridge of 15 Bridges at the intersection of two canals is among the most spectacular, with a view of a series of stone spans whose arches are gracefully lit at night. The city also has hidden gems that require guidance or tips to find: Some gardens, tucked away in courtyards or behind stately apartments, are open to the public any time, while others open on a special day of the year. The Rijksmuseum, with its Rembrandts and Vermeers, costs $14 entry, but its garden is open year-round for free. The Begijnhof is a grassy courtyard surrounded by 14th century cottages — an oasis of quiet at one of the busiest sections of town. Near the Begijnhof is a covered passageway known as the Civics Guard Gallery, with 15 huge group portraits — from the same time as Rembrandt's Night Watch — of leading citizens from the Dutch Golden Age. Outside the well-trod shopping lanes are the lesser known sections, like the “Nine Lanes,” lined with tiny specialty establishments like the handmade soap shop, the spectacles museum and a store dedicated to toothbrushes. The city's 26 open-air markets offer knickknacks, antiques, farmers' produce, artworks, clothing and just about anything else you can think of. Traveling by bicycle makes you feel like a true local. About 40 percent of Amsterdam traffic is on two wheels. Most streets have special lanes and traffic lights — and woe be to the unwary pedestrian who walks in the bike path. Although the bicycle is king in Amsterdam, beware of the many trams and getting your wheel caught in their rails. Tourists can rent a bike for about $13 a day, with special weekly rates. Also available are tandems for two, cargo bikes for hauling groceries or toddlers, and bikes with child seats. Biking opens up the prospect of escaping the urban setting for a countryside of pastureland, windmills and more canals. On the southern side of the city is the 2,500-acre Amsterdam forest, the city's largest park with more than 30 miles (50 kms) of bike paths. Things to do Visitors wanting to get the most from the city would be advised to buy a travel card, known as an “I amsterdam” card, which gives free access to dozens of museums, free public transport, one free canal cruise, and 25 percent discounts on many concerts and restaurants. A 24-hour card costs $50, going up to $75 for a three-day card. A one-hour canal cruise with a recorded explanation in several languages costs $9.80 but you can buy a hop-on-hop-off day pass with 14 stops for $23.50. The St. Nicolaas Boat Club, a nonprofit group that preserves old boats and barges, offers free rides. Amsterdam's museums include some of Europe's finest, including the Gothic Rijksmuseum and the modern Van Gogh Museum. Rembrandt House has been restored to its 17th century appearance when the artist lived and worked there, but houses none of his great paintings. Here's a tip: Avoid the crowds and look for those days when the museums are open in the evenings. Those are just the best known of more than 40 museums. There also are the Museum of Bags and Purses and the Torture Museum. You don't have to go to a museum to see fine art and antiques. The Spiegelstraat, the street leading up to the main door of the Rijksmuseum, has the first rank of the city's 140 art galleries. For contemporary art, several times a year Dutch artists open their studios for an open house or hold free exhibitions on Saturdays and Sundays. Amsterdam's concerts and operas usually are not for the budget traveler. But in summer you can catch free half-hour lunchtime concerts twice a week, once in the ornate Concert House and once at City Hall. Where to Stay Hotels are expensive, but backpackers can stay in a hostel dormitory for $26 a night. Families might find a bed-and-breakfast in an apartment or even a houseboat for a reasonable price. Good last-minute deals can be had at many hotels during the off season. Dining Look for small restaurants classified as “eetcafes.” Often they serve hearty ethnic meals. Dutch food from kiosks is cheap and clean. Typical Dutch herring, raw with onions and pickles, is a local favorite for $3.25 a serving. Dutch pancakes, which can be a meal in itself, cost $5.20 and upward depending on the topping.