The medieval core and the seventeenth-century canal ring: the postcard Amsterdam, the most crowded, and still worth your time if you handle it well.
Centrum is the Amsterdam everyone arrives for - the ring of canals, the gabled houses, Dam Square, the old harbour front and the red-light lanes. It is compact, walkable and stuffed with the city's headline sights, and it is also where the crowds, the noise and the tourist traps concentrate. The trick is to use it deliberately: see the things worth seeing, then step out into the quieter districts around it.
The medieval town and the canal ring (Grachtengordel) around it, from Centraal down to the Amstel.
The centre is two layers. The medieval town is the oldest part, around the Oude Kerk (begun around 1306, the city's oldest building) and the Nieuwmarkt with its turreted Waag. The streets here are tight and slightly tangled, following the medieval plan.
Wrapped around it is the Grachtengordel, the ring of canals - Herengracht, Keizersgracht, Prinsengracht - dug in the seventeenth century during the city's golden age and listed by UNESCO since 2010. This is where the merchant houses line the water, tall and narrow because they were taxed on width, topped with the step, neck and bell gables that give the city its profile. Dam Square holds the grandest single building, the seventeenth-century town hall that is now the Royal Palace.
You come to the centre because the famous things are here and many of them earn it: walking the canal ring at a quiet hour, the churches, the Begijnhof courtyard, the view from a bridge over three more bridges. It is small enough to cross on foot, which is the right way to see it.
Be honest about the rest. The red-light district (De Wallen) is a real piece of the city's history wrapped in a lot of stag-party tourism, and the souvenir strips around the Damrak and Leidsestraat are best walked through quickly. The good move is to see the centre early or late and eat and drink elsewhere.
The centre is safe in the sense that violent trouble is rare, but it is the part of Amsterdam where you most need ordinary street sense. Pickpockets work the crowds on the Damrak, around Centraal, on packed trams and in the red-light lanes. Late at night the bar quarters around De Wallen, Leidseplein and Rembrandtplein get drunk and rowdy. Mind your bag, watch the bike lanes when you step off a kerb, and the centre gives no real trouble.
Yes, in general. Serious crime is uncommon, but it is the most pickpocket-prone part of the city, especially around Centraal, the Damrak and the red-light district and on crowded trams. The bar areas get loud and drunk late at night. Keep an eye on your belongings and you will be fine.
The Grachtengordel, the ring of seventeenth-century canals - Herengracht, Keizersgracht and Prinsengracht - dug during Amsterdam's golden age and a UNESCO World Heritage site since 2010. The tall, narrow gabled merchant houses along them are the classic Amsterdam view.
It puts you next to the main sights, but it is the busiest, noisiest and priciest area, and the streets near the red-light district are loud at night. Many people prefer to sleep in a calmer district like De Pijp, Oost or the Jordaan and walk or tram into the centre.