Explore a comprehensive lecture on localizing invariants and algebraic K-theory presented by Georg Tamme from the University of Mainz. Delve into the fundamental insights of Thomason, building upon Waldhausen's work, which define algebraic K-theory through the category of perfect complexes. Examine how K-theory transforms Verdier quotient sequences into fiber sequences of spectra, establishing it as a localizing invariant. Investigate the descent properties of K-theory and other localizing invariants, including Nisnevich descent. Journey through classical topics in the field and discover recent developments and applications, with a particular focus on algebraic K-theory. The lecture covers key concepts such as classical K-theory, incompletion, non-connective K-theory, Schlitting, and includes proofs, corollaries, and counter-examples to deepen understanding of this complex mathematical subject.