Object-Orientation FAQ

A class is a general term denoting classification and also has a new meaning
in object-oriented methods.  Within the OO context, a class is a specification
of structure (instance variables), behavior (methods), and inheritance
(parents, or recursive structure and behavior) for objects.  As pointed out
above, classes can also specify access permissions for clients and derived
classes, visibility and member lookup resolution.  This is a feature-based or
intensional definition, emphasizing a class as a descriptor/constructor of
objects (as opposed to a collection of objects, as with the more classical
extensional view, which may begin the analysis process).

Original Aristotlean classification defines a "class" as a generalization of
objects:
[Booch 91, p93]
  "a group, set, or kind marked by common attributes or a common attribute; a
   group division, distinction, or rating based on quality, degree of
   competence, or condition".
[Booch's definition in the context of OOD]
  "A class is a set of objects that share a common structure and a common
  behavior."  "A single object is simply an instance of a class."

The intension of a class is its semantics and its extension is its instances
[Martin 92].

[Booch 94, 4.2] proposes 3 views of classification as useful in OO analysis and
design: classical categorization (common properties), conceptual clustering
(conceptual descriptions), and prototype theory (resemblance to an exemplar).
He advocates starting with the former approach, turning to the second approach
upon unsatisfactory results, and finally the latter if the first two approaches
fail to suffice.