Starting with an updated description of Allen's calculus, the bookproceeds with a description of the main qualitative calculi whichhave been developed over the last two decades. It describesthe connection of complexity issues to geometric properties. Modelsof the formalisms are described using the algebraic notion of weakrepresentations of the associated algebras. The book also includesa presentation of fuzzy extensions of qualitative calculi, and adescription of the study of complexity in terms of clones ofoperations.