In this 1 hour and 44 minute lecture from the ICTP-SAIFR Minicourse on Partial Differential Equations: Analytical and Numerical Tools, Professor Oscar Reula from the National University of Córdoba, Argentina, explores the critical topic of energy estimates. Delve into mathematical techniques for analyzing partial differential equations through energy-based approaches, which are fundamental for establishing existence, uniqueness, and stability of solutions. This class represents the 16th session in the comprehensive minicourse scheduled from May 5 to June 30, 2025. Learn advanced analytical methods that form the cornerstone of modern PDE theory and their applications in mathematical physics.