The most common religion in Iceland nowadays is Lutheran. Also Hallgrímskirkja in Reykjavik downtown is a Lutheran church.

Hallgrímskirkja was built in the mid 20th century. Which is quite late for someone coming from Austria. Like most Lutheran churches the architecture is simple but beautiful. The architecture reminds of the Icelandic landscape like basaltic columns, mountains and rocks. The pipe organ is made in Germany. In front of the church Leifur Eriksson who was the first Icelander and some might say even the first European to sail to America.

I would recommend to buy a ticket (1,200ISK) for the elevator which brings you to the top of the tower. This is the best view point over Reykjavík within the city.