Explore the fascinating world of complexity through the lens of modern statistical mechanics in this 67-minute lecture by Constantino Tsallis from the Centro Brasileiro de Pesquisas Fisicas and Santa Fe Institute. Delve into the study of natural, artificial, and social systems using concepts from nonextensive statistical mechanics, which generalizes the Boltzmann-Gibbs-Shannon-von Neumann entropy through nonadditive entropies. Discover the physical motivations behind this generalization and examine its applications across various fields of knowledge. Gain insights into the progress made since 2005 when Murray Gell-Mann and Tsallis investigated q-triplets, and understand the advancements achieved in this area of complexity science.