Explore the intricate “Inverse Galois Theory” by Springer Monographs in Mathematics, now in its comprehensive second edition. This essential volume delves into the profound question of which finite groups manifest as Galois groups over a specified field. It meticulously examines the structure and representations of the absolute Galois group of K, and its finite epimorphic images, central to the inverse problem of Galois theory. Discover groundbreaking advancements, particularly the rigidity method and its applications, alongside systematic overviews of new existence theorems and construction methods for Galois extensions. This edition highlights two major developments: the algebraization of the Katz algorithm and the emergence of modular Galois theory, offering novel approaches for fields of positive characteristic. Ideal for mathematicians and researchers seeking advanced insights into Galois theory.