The present proposal of a Mathematical Theory of Sustainability and Sustainable Development starts from the review of several currently accepted scientific theories Fuzzy Logic, Systems Theory, Complexity Theory, Chaos Theory, Ecology, Decision Theory, etc...] and arrives at conceptualizing sustainability in relation to each of them. Based on this review and conceptualiza-tions, a System of Definitions and Axioms is proposed, from which we deduce a procedure and mathematical formulations to model and measure the Sustainability Degree of systems. The applications of the conclusions of this theory are numerous, including assessing ecological systems or any social organization companies, cities, regions, countries...], informing us both of their 'optimality' as their 'probability to endure', providing a parameter that will be possible to apply in many common decision making processes.