From the Carlitz Exponential to Drinfeld Modular Forms

This paper contains the written notes of a course the author gave at the VIASM of Hanoi in the Summer 2018. It provides an elementary introduction to the analytic naive theory of Drinfeld modular forms for the simplest ‘Drinfeld modular group’ GL2(q[ θ] ) also providing some perspectives of development, notably in the direction of the theory of vector modular forms with values in certain ultrametric Banach algebras