Finite Fields

The book focuses on the significance of finite fields in various mathematical disciplines, particularly highlighting their applications in coding theory and cryptography. It delves into the Normal Basis Theorem, a pivotal concept in field theory that asserts the existence of a specific element in finite dimensional Galois extensions. The text also reflects on the historical development of this theorem since its initial proof by K. Hensel in 1888, emphasizing its modern relevance in arithmetic computations and ongoing research in finite field theory.