The complex realm of transcendental numbers is examined in this subject, along with its characteristics, relationships to other branches of mathematics, and practical uses. The study starts with a summary of transcendental number theory, including its historical evolution, salient characteristics, and important mathematical applications. To provide clarity and depth, the fundamental elements—such as the Lindemann–Weier strass theorem and the terminology essential to comprehending transcendental numbers—are expanded upon. Transcendental numbers are useful in physics, computer science, and encryption, as shown by the study's practical scientific applications. A thorough approach to comprehending, evaluating, and using transcendental numbers is provided via the main strategies used, which include a literature survey, comparative analysis, algebraic procedures, and logical reasoning.