Sort Posts by Category

Hi,

I’m trying to list post by categories. I’ve found that this is possible in several ways, but none of them work as desired. I’m trying to make a loop that lists the posts like this:

Category
post-title,post-title,post-title, etc

Category2
post-title,post-title,post-title, etc

Category3
post-title,post-title,post-title, etc

Hardcoding this and making a custom loop for each category is easy, but doing a custom loop that echoes each category and it’s posts is giving me a headache.

Any clues on how to approach this?

Thanks!