Þykkvabæjarklaustur, farm, church and a monastery from 1168 until the Reformation in the 17th century. Its first abbot was Þorlákur Þórhallsson the Holy, the only Icelander to have been canonized by the Roman Catholic church, which was confirmed by the Pope in 1984. The 23rd of December is Þorláksmessa, his saints day. Plaque commemorating the monastery can be seen where the altar once was. In the sands above the farm a very big medieval farmstead which was buried in a flood from Katla has been dug up. About 6 km distance south of Þykkvabæjarklaustur on an almost impassable path are two sheephouses of turf from about 1900. One of them has lymegrass between rafters and turf roofing and a unique type of timber frame. In the keeping of the National Museum since 1974.