HCL classes fall into four groups:

• Core classes: pure virtual base classes (interfaces) expressing the basic concepts of calculus in Hilbert space: vectors, vector spaces, operators, functions, Cartesian products.
• Algorithm classes: implementations of linear algebra and optimization methods using the HCL core classes.
• Concrete classes: instantiable vector and operator classes useful in scientific programming.
• Tool classes: "bridge" or "wrapper" classes, providing methods which combine HCL objects to produce new HCL objects, also utility classes for memory management etc.

Each class is documented. Documentation includes a brief overview of the function and usage of the class, and detailed descriptions of all public methods and their signatures (names, argument types, return types). The documentation is organized by header file: some header files describe only one class, others several related classes.