In the context of object-oriented design, software systems model real-world entities abstractly represented in the system classes. As the system evolves through its lifecycle, its class design also evolves. Thus, understanding class evolution is essential in understanding the current design of the system and the rationale behind its evolution. In this paper, we describe a taxonomy of class-evolution profiles, a method for automatically categorizing a system's classes in one (or more) of eight types in the taxonomy, and a data-mining method for eliciting co-evolution relations among them. These methods rely on our UMLDiff algorithm that, given a sequence of UML class models of a system, surfaces the design-level changes over its lifecycle. The recovered knowledge about class evolution facilitates the overall understanding of the system class-design evolution and the identification of the specific classes that should be investigated in more detail towards improving the system-design qualities. We report on two case studies evaluating our approach.