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Delve into the second class of a comprehensive minicourse on quantum gravity, presented by Manuel Asorey from the University of Zaragoza, Spain. Explore both perturbative and nonperturbative approaches to quantum gravity problems in this 1 hour and 47 minute lecture. Gain valuable insights into the fundamental concepts and challenges of merging quantum mechanics with general relativity. Part of a series organized by ICTP-SAIFR from May 20-24, 2024, this class offers an in-depth look at the cutting-edge field of quantum gravity, essential for advanced physics students and researchers interested in the frontiers of theoretical physics.