Lease agreements and lease register.

Lease agreements can be found on the website of Húsnæð og manvirkjastofnun (HMS). Lease agreements

Tenants can register their leases electronically in HMS's lease register. Electronic registration of a lease is a prerequisite for being able to apply for housing benefits. Electronic registration of leases

According to Article 53 of the House Renting Act, you have the right of priority on the premises you rent and the right to reject contractual increases.