Grundtvigs Kirke (or Grundtvig's Church) is a much photographed, though not as often visited, church to the northwest of central Copenhagen. While it's a bit off the beaten path, it's only about a 20-minute bike ride from the city center (the journey is longer if you travel there on public transportation, but do as the Danes do, and get on a bike).
Architect Peder Vilhelm Jensen-Klint's design won a competition for the church commission in 1913, but World War I delayed construction until 1921. It was completed in 1940. (Jensen-Klint was also responsible for the surrounding residential development.) The building is notable as a rare example of a church constructed in the Expressionist style. Its monumental and severe exterior was inspired by traditional Danish churches, while the interior is a soaring space filled with light that pours in, on sunny days, through the clear windows and illuminates the pale yellow bricks used in its construction.
If you plan on visiting, this is an active church and it is open only to those attending services until noon on Sundays (and then closes at 4 pm). All other days it is open from 9 am to 4 pm, on Thursdays until 6 pm.