The idea of hyperbolic polynomials first came out from the research of PDE’s. It then drew rather more the attention of people working in optimisations and algebraic geometry. In this talk, we will first go over some basic definitions and notions of such polynomials. Then I will give some simple examples and see a conjecture (Lax conjecture) related to one of them. I will also briefly talk about people’s efforts on the generalisation of the conjecture during the late years. If time permits, some work of my supervisor, Simone Naldi, would be mentioned. This talk could be regarded as a prequel of the one given on 15/02/2018 in our team.