Towards the mathematics of quantum field theory

We will give an introduction to the methods of the book "Towards the mathematics of quantum field theory". One may sum-up these methods by saying that the geometry of the physicists "spaces of fields" can be studied either by a coordinate (i.e. algebraic or analytic) approach, or by a parametrized (i.e., geometric) approach. Both approaches are complementary, and the aim of categorical methods in geometry are to improve them by introducing new types of algebras and new types of spaces, in a way that is adapted to the study of both algebraic and geometric obstruction problems. Since such obstruction problems are widespread in quantum field theory, these new methods give a kind of "geometry of obstructions", that gives a way to understand obstruction theory in a geometric manner.