Stadsarchief (City Archive) is an institution that shows the history of Amsterdam in different expositions throughout the year. Entrance to the basement is free. Other expositions cost money, but are worth it. Also worth a look from the outside. Built in the style of Amsterdam School (brick expressionism) in the 20's, it is a true eye-catcher.
Visit the Stadsarchief if you want to dig into the history of Amsterdam and get to know the city's hero's. You can see very old, but interesting footage of the city from the 20's and on. A lot of nice portraits of the canals through the years.
A guided tour costs only €4.