This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions f : R → R, with the notion of continuity, and the construction of the derivative f ′ (x) and of the integral b a f (x)dx. Then we investigate the case of the complex functions f : C → C, and notably the holomorphic functions, and harmonic functions. Then, we discuss the multivariable functions, f : R N → R M or f : R N → C M or f : C N → C M , with general theory, integration results, maximization questions, and basic applications to physics.