2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159436This text is a survey of recent results obtained by the author and collaborators on different problems for non-self-adjoint operators. The topics are: Kramers-Fokker-Planck type operators, spectral asymptotics in two dimensions and Weyl asymptotics for the eigenvalues of non-self-adjoint operators with small random perturbations. In the introduction we also review the notion of pseudo-spectrum and its relation to non-self-adjoint spectral problems.Spectral TheoryAnalysis of PDEs35P20; 35K65; 35Q99; 35S99text