Algebraic specifications of data types provide a natural basis for testing data types implementations. In this framework, the conformance relation is based on the satisfaction of axioms. This makes it possible to formally state the fundamental concepts of testing: exhaustive test set, testability hypotheses, oracle. Various criteria for selecting finite test sets have been proposed. They depend on the form of the axioms, and on the possibilities of observation of the implementation under test. This last point is related to the wellknown oracle problem. As the main interest of algebraic specifications is data type abstraction, testing a concrete implementation raises the ishe gap between abstract description and concrete representation. The observational approaches of algebraic specifications bring solutions on the basis of the so-called observable contexts. After a description of these methods, the chapter gives a brief presentation of some tools and case studies, and presents some app...