21 year old law student looking for accomodation in Reykjavik

Hi!

I and my girlfriend are looking to spend the summer holidays working in Reykjavik. For that we need accomodation. As we are both broken students, we are looking ideally for the cheapest option, that is to say a shared apartment with other people. We are planning to stay in Iceland from July to early September which is when I can imagine some students will leave their rooms empty. We could fill those empty rooms and pay your rent!

We both are rather silent people immersed in books for most days. I study law, Katarina currently studies medicine. We are intrigued my contemporary art. 

Thank you in advance! If you have any tips how to find accomodation, please feel free to share them with me!

Štěpán