Explore toric varieties as algebraic quotients, exponential actions, Gale duality, and moment-angle manifolds in this 1-hour 3-minute lecture by Taras Panov from Moscow State University. Delivered on July 25, 2024, as part of the "Graduate School on Toric Topology" and the "Focus Program on Toric Topology, Geometry and Polyhedral Products" at the Fields Institute, this talk delves into advanced concepts in algebraic geometry and topology. Gain insights into the intricate relationships between toric varieties and their representations as quotients, understand the role of exponential actions in this context, and discover the applications of Gale duality. Additionally, learn about moment-angle manifolds and their significance in toric topology.