Explore the concept of systems with Hilbert space fragmentation in this hour-long lecture by A. Hutsalyuk from ELTE. Delve into the intricacies of integrability in Condensed Matter Physics and Quantum Field Theory, gaining insights into how fragmentation affects the behavior of quantum systems. Examine the mathematical foundations and physical implications of Hilbert space fragmentation, and discover its relevance to current research in quantum physics and condensed matter theory.