The Thingeyrar monestary was founded by Jon Ogmundsson bishop of the northern see in 1112, but there are no records of monestary life there until 1133, when Vilmundur Thorolfsson was ordained its firs abbot. It was a Benedictine monestary up to the reformation.
Vague ancient sources mention hermits in Iceland before Christianity was adopted and cloisters were established. One of the stories tells us about Asolfur Konalsson from Ireland. He did not want company with pagan people. Jorundur the Christian is also mentioned. Mani the Christian is supposed to have built a church at Kolgumyrar in the Hunavatn-county and served there 24 hours a day. Some female hermits are mentioned: Gudrun Osvifursdottir (she was young when Christianity was adopted; Laxdaela Saga), Hildur, who became a hermit at the Holar Cathedral during the time of bishop Jon Ogmundsson, Groa Gissurardottir (Gissur was the son of Isleifur Gissurarson, the country’s first bishop), who reclused herself when she grew old at Skalholt, Ketilbjörg lived in recluse at Skalholt during bishop’s Pall Jonsson (†1202), and Katrin reclused herself at Munkathvera before the convent at Reynisstadur, where she became the first abbess, was established.
Old sources imply that Hroflur (Rudolf) established a monestary at Baer in Borgarfjordur close to the year 1030. He was called back to England in 1049. There were more attempts at establishing cloisters during the early years of the church. Bishop Magnus Einarsson at Skalholt bought a part of the Westman Islands and attempted the establishment of a monestary there. He was lost in a fire in 1148 and nothing came off his ideas. Jon Loftsson at Oddi built a monestary at Keldur around the year 1190, where he wanted to spend his last years. It was probably abandoned after his death in 1197.