Explore the fundamentals of complexity and mean-field theory in this comprehensive lecture by Letícia Cugliandolo from Sorbonne Université, France. Delivered as part of the São Paulo School of Advanced Science on Disordered Systems organized by ICTP-SAIFR, this first class in the series provides essential insights into theoretical approaches for understanding complex systems. The lecture spans 1 hour and 43 minutes, offering in-depth coverage of mean-field theoretical frameworks that are crucial for analyzing disordered systems. This educational session was conducted as part of the April 28 - May 9, 2025 program at ICTP-SAIFR.