Aircrafts, trains, cars, plants, distributed telecommunication military or health care systems, and more, involve systems design as a critical step. Complexity has caused system design times and costs to go severely over budget so as to threaten the health of entire industrial sectors. Heuristic methods and standard practices do not seem to scale with complexity so that novel design methods and tools based on a strong theoretical foundation are sorely needed. Model-based design as well as other methodologies such as layered and compositional design have been used recently but a unified intellectual framework with a complete design flow supported by formal tools is still lacking. Recently an “orthogonal” approach has been proposed that can be applied to all methodologies introduced thus far to provide a rigorous scaffolding for verification, analysis and abstraction/refinement: contractbased design. Several results have been obtained in this domain but a unified treatment of the topic that can help in putting contract-based design in perspective is missing. This paper intends to provide such treatment where contracts are precisely defined and characterized so that they can be used in design methodologies such as the ones mentioned above with no ambiguity. In addition, the paper provides an important link between interface and contract theories to show similarities and correspondences. This paper is complemented by a companion paper where contract based design is illustrated through use cases.