This volume includes the lecture notes of the three mini-courses that have been given during the CIRM-SMF week entitled Inhomogeneous Flows: Asymptotic Models and Interfaces Evolution that took place at the CIRM from September 23 to September 27, 2019. The conference followed the themes of the ANR-15-CE40-0011 INFAMIE project and aimed at bringing together experts coming from various branches of mathematical fluid dynamics and interested in inhomogeneous fluids where problems of interfaces occur. Beside the mini-courses, the event comprised 14 plenary talks that were specifically dedicated to inhomogeneous flows.

The mini-courses emphasized on the one hand theoretical approaches that proved to be efficient in the study of evolutionary fluid mechanics (maximal regularity issues in the notes of P. Kunstmann with stress on the $L^1$-in-time estimates that turn out to be crucial in the study of free boundary problems, and the prospective course by P. Auscher on tent spaces), and on the other hand the modeling aspect with the lectures by S. Gavrilyuk devoted to the derivation of models of bi-fluids by means of Hamiltonian principle.

The originality of these texts is that they have been written conjointly by the speaker and young participants, from the notes that have been taken during the courses.