An introduction to enumerative and bijective combinatorics with binary trees - Prof. Xavier Viennot

Trees and branching structures are everywhere in nature. Their mathematical abstraction leads to the notion of binary trees, a basic notion in computer science. The simple question "how many binary trees with n nodes", will give us the opportunity to travel from old and classical combinatorics to nowadays enumerative combinatorics. 
Its « philosophy » can be summarized in the following: « replacing calculus by figures and bijections, or conversely making calculus from the visual figures ».