In this book, I will be guiding you through many examples using Hammer. There are a handful of terms that will recur many times that you will need to know. It might be a good idea to bookmark this page, so you can flip back and refresh your memory.
A brush is a piece of world geometry created with block tool. Brushes make up the basic building blocks of a map and must be convex. A convex object's faces cannot see each other, while a concave object's faces can. Imagine if you're lying on the pitched roof of a generic house. You wouldn't be able to see the other side of the roof because the profile of the house is a convex pentagon. If you moved the point of the roof down inside the house, you would be able to see the other side of the roof because the profile would then be concave.
This can be seen in the following screenshot:
Got it? Good. Don't think you're limited by this; you can always create convex shapes out of more than one brush.
Since we're talking about houses, brushes...