Gear
So, there I was, going for a walking holiday the first time in my life. I had no clue as to what to bring with me. See the right column on what I actually brought with me. Below, I spend a few lines on how I experienced all this stuff.
Footwear
In summer, the terrain in Spitsbergen varies from extremely hard and rough to extremely soft and swampy.
Therefore, both trekking shoes and rubber boots should be part of the basic gear.
For crossing rivers, neoprene diving shoes combined with Teva sandals can also do the trick.
Gaiters are extremely useful when you need to cross a shallow river but don't want to change to rubber boots.
Just make a run for it and they will keep you dry.
Also, they can keep your lower legs warm when your pants are a bit too short.
If you're planning to cross a glacier or walk on ice in general, bring crampons. Make sure your shoes are suitable for them.
I never got to trying them out, as reaching our glacier was merely impossible because of the rough melting water.
Clothing
During summer, the temperature varies from 0 to 10 degrees Celsius, which makes it very hard to decide what to wear. I skipped the thermal underwear. Too hot. Just a T-shirt, fleece and windjacket was enough.
When it got windy, I put on my hat and scarf. This keeps your head warm, and a warm head means a warm body.
Tundra's can be really really wet up to over your knees, so expect to get your feet wet at anytime. Therefore, bring a pair of extra socks on each trip.
Containers
As I did daytrips, I brought a big backpack for storing and a small one to carry stuff. The small one has a 3 liter water container. I did not carry that around, as on Spitsbergen you can drink all water given by nature. The water container was extremely useful for storing water for cooking, though.
I was one of the lucky who brought a raincover/travelbag for my big backpack. During the boat transfer, the sea got pretty rough and all luggage on the boat got pretty wet. Except mine. Such a raincover/travelbag also prevents airport personnel from tearing straps or strings off your backpack.