>>567197>Single person tent, sleeping bag, a mat, inflatable pillow.check, make sure the sleeping bag is in a waterproof bag.
>Mountain bike, pump, oil/grease. add a tube to that and some pliers
>Two pairs of shoes, pants, some shirts, a sweater, waterproof jacket, socks, underwear.add swimming trunks, rain trousers, wool cap, wool shirt and mid-layer (fleece, wool) and some gloves to that. It can (and likely will happen) that temperatures drop to near 0, some rain and heavy wind. make sure your stuff is is in a watertight folding bag.
>A knife(thinking of taking a swiss knife too not sure yet), lighter, matches, routed map, compass.check
>Portable stove, shampoo, soap, metal cup and bowl/pot, cooking pot, rope.add water bottles / bags and spoon, rope only needed for highlands
>Camera, notebook, few books, batteries, signal flare, old phone for emergency contact, tarpaulin.check,
>Rest will be filled with canned food and water.Try delicious Icelandic Hardfiskur, air dried fish fillets, 83% pure protein. Also the local rye bread is es excellent power food. I'd recommend to add some pasta and pesto sauce, along with cheese. I'd recommend to drop the canned food for fresh one, that is if you keep to the lowlands, you can restock daily, and Icelandic local products are just great.
Also chocolate and a bottle of something are a good idea. And for fucks sake bring some tea, nothing as good as a cup of tea on a cold miserable day in Iceland.
http://www.safetravel.is/ has good info
their gear recommendation:
http://www.safetravel.is/wp-content/uploads/2010/12/jun-equipment-list-joined.pdf 
