Introduction Welcome to the Math SOMMa Junior Meeting 2024. This event is dedicated to early-career researchers, including predoctoral and postdoctoral researchers, and aims to enhance collaboration among the prestigious Severo Ochoa and Maria de Maeztu research institutions in mathematics; the Basque Centre for Applied Mathematics (BCAM), Instituto de Ciencias Matemáticas (ICMAT), Instituto de Matemáticas de la Universidad de Granada (IMAG), Centre Internacional de Mètodes Numèrics a l’Enginyeria (CIMNE), and the Centre de Recerca Matemàtica (CRM). Our diverse program is designed to stimulate intellectual exchange and networking. It features a mix of plenary sessions, contributed talks, and a dynamic poster session. Alongside these, we have planned a series of complementary activities to foster networking and collaboration. We warmly invite you to be an active participant, whether by presenting your latest research, joining in enriching discussions, or simply immersing yourself in this engaging community. Join us in Barcelona for an unforgettable experience of learning, collaboration, and growth!