Explore the innovative Echo Method for detecting axion dark matter in this 59-minute lecture by Elisa Todarello at the Galileo Galilei Institute. Delve into the fundamental concepts of the echo idea, decay rates, and stimulated decay as Bose-enhancement. Examine the enhancement factor and analyze the characteristics of echo waves, including their appearance and properties. Investigate the echo power at ground level and learn about a model for the beam, considering both small and large velocity dispersions. Discover the collected power and sensitivity of this detection method, and understand the importance of beam height. Conclude by exploring two types of antennas used in this groundbreaking approach to dark matter detection.