Þykkvabæjarklaustur is a present and historic church site snuggled in the Álftaver pseudo crater area. In medieval times this was the location of a catholic monastery, which was founded in 1168 and remained active until the reformation in the mid-16th century. Recent archaeological findings (2015) show that there was an extremely large building of about 1800m2 of ground floor. It was a rich convent of monks with a large farm and a school.