  These five lectures on undecidability were given to students with a good
level in mathematics but with no special knowledge on logic. The first
conference presents the formalization of mathematics with a short historical
survey, the language of first order predicates and the axioms of set theory.
The second and third lectures explain the incompleteness phenomena from the
Hilbert program until G\"odel's theorems with a presentation of the sequent
calculus of Gentzen.The fourth talk deepens model theory reasoning in the case
of the continuum hypothesis, and the last conference gives examples of
effective computability results.
