The official municipal archives of Amsterdam (that frequently organizes exhibitions and lectures).
There is a (freely accessible) shop with i.a. books and postcards.

The Stadsarchief houses many archives related to Amsterdam, and also has an extensive collection of old maps and photographs.

This is also the place to start if you're doing genealogical research. The Stadsarchief has the birth certificates and marriage registries of Amsterdam inhabitants.

One of the most important items in the Archives' possession is the Tolprivilege. This document dates from October 27, 1275 and mentions the name Amsterdam for the first time. And therefore, October 27 is considered to be Amsterdam's 'birthday'.
It is shown to the public every year for a few days around October 27.

The building is a design of the architect Karel de Bazel, from the 1930's. It used to be a bank.

There is a cafe inside.

Address:
Vijzelstraat 32, Amsterdam
Web:
http://stadsarchief.amsterdam.nl

Opening hours:
Tu-Fr 10-5, Sa-Su 12-5
Closed on New Year's Day, December 25 and King's Day.
Tickets:
Go into the building, once you're in the hall, turn to the left.
Closed on 26 April (Kings Day), 25 December and 1 January.

Entrance fee:
Access to the archives is free, but if there is an exhibition there is normally a fee for that.