The course aims at presenting the modern mathematical tools used in the study of micromagnetics. This topic lies at the interface between Partial Differential Equations (PDE), Calculus of Variations and Mathematical Physics. More precisely, micromagnetics is the continuum theory of magnetic moments underlying the description of magnetic structures and it is based on a variational principle that is nonconvex, nonlocal and multiscale. The plan is to analyse the pattern formation in ferromagnetic materials, in particular, domain walls, vortices, skyrmions etc. This study raises fundamental mathematical questions (regularity, uniqueness, symmetry, stability, asymptotic analysis etc.) for which various techniques will be presented coming from elliptic PDEs, theory of harmonic maps, scalar conservation laws, Γ-convergence, theory of Ginzburg-Landau etc. Other information may be found here. The course is supported by INdAM. Schedule: from 16/01/2026 to 14/02/2026, every Tue & Fri, 14:00-16:00. Intereseted students are invited to contact the Lecturer (radu.ignat@math.univ-toulouse.fr)