Yeah, Svalbard is the archipelago and Spitsbergen is the largest island, followed by Nordaustlandet, Edgeøya .. and Bjørnøya and lots of tiny islands.
Longyearbyen on Spitsbergen is the northernmost city in the world that has a proper infrastructure (police, fire department, people governing, yadda yadda).
In the picture, I'm actually on my way to one of my sites. When the snow melts, the water can't seep very far into the ground because of the permafrost, so you get these annoying rivers popping up all over the place in the valleys. It's annoying! That one's just a stream compared to some of the bigger ones .. and having to take off your pants to wade through meltwater river is not always pleasant .. >.<
I didn't have to do that to get to any of my sites, luckily. But I always got wet feet on the way back.
I know several germans who I've studied biology with on Svalbard. 3 of them were from Kiel .. Where do you live in Germany?