This church was build in 1958-1962 and is the symbol of the Kópavogur area. This acropolis of the less interesting Kópavogur center area is a beautiful landmark and the residents of the city are very proud of it.
The opening times are quite variable, but then again the main attraction is probably the lovely view to the Reykjavik area as well as the souther greater Reykjavík area. The rocky area around the church are inhabited by elves.
Better call beforehand if you want to enter the church, as opening times are quite fuzzy.