I have attempted to look at the Primer from the viewpoint of non-specialized user that want to understand what OWL is about and whether it would be useful for them. Some sections seem to work, other don't. The section on basic notions is good, but needs a bit more explanation in some places. However, when looking at the overall organization it seemed to me that the Primer should answer some specific questions. I have given a shot at these questions and an idea for the shape of the answer. If these are the right questions then the questions determine the outline.
What is the purpose of the document?
Introduce OWL 2 to a general, non-specialized audience
2. What is OWL 2
Proposed W3C standard, …
3. What is the intent or purpose of OWL 2?
Knowledge representation language, e.g., for modeling real world phenomena
4. What is the history of OWL?
Heritage of KR languages and DL
5. What are the design criteria for OWL?
Interoperability – data interchange formats
6. What are the basic notions?
Instances, classes, relations, datatypes
7. What are some applications of OWL?
Life sciences, systems engineering, information management
8. What is the syntax?
Note that multiple concrete syntaxes are possible
Minor point - is the Primer about OWL 2 or OWL 1? There is some inconsistency in usage.