In this sixth class of the ICTP-SAIFR Minicourse on Partial Differential Equations: Analytical and Numerical Tools, Professor Oscar Reula from the National University of Córdoba, Argentina, explores the concept of infinite dimensional vector spaces. Delve into advanced mathematical concepts essential for understanding partial differential equations through this comprehensive 2-hour and 19-minute lecture. The session is part of a broader educational program scheduled from May 5 to June 30, 2025, designed to equip participants with both analytical and numerical approaches to PDEs. For additional information about the complete minicourse and registration details, visit the ICTP-SAIFR website.