The Amsterdam Museum has a lot of archeological finds and old art relating to Amsterdam, but also collects modern material.
In 2010 it changed its name from Amsterdam Historical Museum to Amsterdam Museum to reflect that it does no longer only focus on Amsterdam's history (but don't let this fool you: it still is mainly a museum about Amsterdam's history).
If you want to find out about the general history of Amsterdam, this museum is a good start.
Giant Goliath in Amsterdam Museum
