The aim of this permanent school is to introduce undergraduate and Ph.D. students in mathematics and physics as well as post-doctoral researchers in a recently emerged area of mathematics and theoretical physics: Secondary Calculus. A diffiety is a new geometrical object that properly formalizes the concept of the solution space of a given system of (nonlinear) PDEs, much as an algebraic variety does with respect to solutions of a given system of algebraic equations. Secondary calculus is a natural diffiety analogue of the standard calculus on smooth manifolds, and as such leads to a very rich general theory of nonlinear PDEs. It appears that it is the only natural language of quantum physics, just as the standard calculus is for classical physics.