We are glad to announce the conference to celebrate 40 years of the seminar of the group in Analysis and Partial Differential Equations at the University of the Basque Country (UPV/EHU) and the Basque Center for Applied Mathematics (BCAM). Mathematical Analysis has a long-standing tradition in the Basque Country, with the group seminar serving as the main gathering point for the community since its inception. Members of this community have made significant contributions to key areas such as harmonic analysis, dispersive equations, kinetic theory, and nonlinear equations, and this event brings together leading specialists in these fields to present the latest developments and foster new directions of research.