In addition to the seven universities in Iceland there are also smaller units offer diplomas on a higher education level. Most of the higher education institutions are run by the state or private parties with state support.
Currently there are approximately 18000 students enrolled in the higher education system, of which about 5% are international students.
International students either attend Icelandic higher education institutions as degree-seeking students or as exchange students. For exchange options, please consult the international office of your home university, where you can get information on partner universities.
You should be able to find something that suits you in one of the links here below.
A good starting point would be the Study in Iceland site giving all the neccisary general information before you get started.