Object of study: the resource calculus (Ehrhard-Regnier 2003) functional programming language based on λ-calculus, explicit handle on the resources used by a program during its execution. Develop an abstract model theory for differential and resource lambda-calculus: definition of model based on category-theory / universal algebra. Mathematical tools for studying the resource calculus: program decomposition through Taylor expansion (link with analysis), natural duality theory for algebraic models (link with topology) Study of definability / adequacy / full abstraction on concrete models: relational semantics: from functional to relational interpretations, game semantics: from static to interactive denotations. Applications: design of functional programming languages with explicit handle of resource consumption and non-determinism