Create Sections From Categories

I can’t seem to find the answer to this issue.
Let’s say I have 100 posts, categorized in 4 different ways, and I want 4 different sections of my site, with these posts in each different section.

How can I do this? With a plug in? Or coded manually?

I hope this is clear what I’m looking for. Just a way to organize my posts into categories, instead of having all of my posts in the same place.

Example blog: http://clockwork-music.com