Explore the intricacies of K-theory in large triangulated categories through this 44-minute lecture by Alexander Efimov, presented by the International Mathematical Union. Delve into key concepts such as Grothendieck groups, categorical localization, and higher algebraic K-theory. Examine the compatibility of definitions and the motivation behind continuous K-theory. Investigate presentable cocomplete categories and dualizable DG categories, including equivalent definitions of dualizability. Learn about the continuous K-theory of nuclear modules through direct computation, and discover practical applications in the field of almost mathematics. Gain a deeper understanding of negative K-theory and K-theory spectra as you navigate this comprehensive exploration of advanced mathematical concepts.