  Symmetric functions provide one of the most efficient tools for combinatorial
enumeration, in the context of objects that may be acted upon by permutations.
Only assuming a basic knowledge of linear algebra, we introduce and describe
the classical toolbox of symmetric functions, and give many examples of their
uses. In particular, we present how classical formulas of enumerative
combinatorics afford a natural generalization in terms of symmetric functions.
We then rapidly present Macdonald symmetric functions and associated operators,
to go on with the description of their relations to rectangular Catalan
combinatorics. We also discuss the link with a realization of the elliptic Hall
algebra, as an algebra of operators on symmetric functions.
