What is the solid crud that appears inside my kettle? Almost every share-house I've lived in has had some nasty looking solids collecting inside.  I always regret looking inside the kettle because a cup of tea never tastes quite as good after you've seen this:



What is that stuff?  What's the physical process that causes it to collect and why is it usually concentrated around the heating element?  Is it related to calcium in tap water, or is there any trick to prevent it appearing in your kettle?  Is it dangerous to ingest and should be removed, or is it harmless?
This is limescale and you have it because your tap water is rich in minerals (mainly, calcium, as you note). You could remove these minerals with an ion exchanger, but you wouldn't to it with a tap water since these minerals give it a better taste. Limescale is not dangerous to ingest, but certainly not pleasant either (and I see on the photo that there is a slot for a mesh that should filter scales). Thick layer of limescale is also bad for the heating element – it hinders heat transfer to water and leads to overheating.

It is a good idea to remove limescale once in a while. You can dissolve limescale with any weak acid, like vinegar, but vinegar smells, so I suggest buying a descaling agent.