Explore the intricacies of reduced Gromov-Witten invariants in this comprehensive lecture delivered by Cristina Manolache at the Galileo Galilei Institute. Delve into the mathematical concepts and theories surrounding these invariants, gaining insights into their applications and significance in algebraic geometry and related fields. Over the course of 1 hour and 12 minutes, examine the fundamental principles, recent developments, and potential future directions in the study of reduced Gromov-Witten invariants.