Explore the fundamental concepts of Lie Groups in this 50-minute undergraduate lecture from Oxford University's fourth-year mathematics program. Learn about these mathematical structures first introduced by Norwegian mathematician Sophus Lie in the 19th century, which have found diverse applications across analysis, geometry, and physics. Discover the basic theory through a variety of concrete examples that illustrate key principles and properties. Gain insight into how Lie Groups serve as a bridge between different areas of mathematics and their practical applications in modern mathematical physics. This introductory lecture provides the foundational knowledge needed to understand more advanced topics in differential geometry and mathematical physics.