Explore the fundamental concepts of tight closure theory in this graduate-level lecture, the first part of a comprehensive overview. Delve into the mathematical intricacies presented by Neil EPSTEIN from George Mason University, USA, as he introduces the foundations of tight closure of ideals and its applications. Gain insights into this advanced algebraic topic, essential for graduate students and researchers in commutative algebra and algebraic geometry. This hour-long session, part of the ICTP Mathematics series, sets the stage for a deeper understanding of tight closure theory and its significance in modern mathematics.