This book explores the essential role of symmetry in physics, with a focus on its dynamic presence in special relativity (SR) and its implications for modern physical theories. By examining symmetry transformations and their connection to conservation laws and covariance, readers gain a comprehensive understanding of these foundational concepts. The chapters cover a range of topics, including the Lorentz group, relativistic transformations, and the covariance of Maxwell's equations. Readers will delve into the mathematical structure of the Lorentz group, its integration with relativistic mechanics, and its application in electrodynamics. Special topics such as Lie groups, the homomorphism with SL(2,C), and the independence of Maxwell's equations are explored, offering a detailed view of the coherence and elegance of the covariant formulation of the Maxwell system. Designed for those with a basic understanding of special relativity and electrodynamics, this book is an advanced supplement to introductory texts. It is particularly beneficial for undergraduate and graduate students, researchers, and academics in physics who wish to deepen their knowledge of symmetry and its significance in high-energy physics. The inclusion of detailed solutions to problems makes it suitable for self-study, providing a valuable resource for anyone interested in the mathematical and theoretical underpinnings of modern physics.