As you can see in this dependency graph, AvalonEdit consists of a few sub-namespaces that have cleanly separated jobs. Most of the namespaces have a kind of 'main' class.
Here is the visual tree of the TextEditor control:
While the main control provides some convenience methods for common tasks, for most advanced features you have to work directly with the inner controls. You can access them using textEditor.TextArea or textEditor.TextArea.TextView.