This book treats a decisive phase in the theological history of the fourth century AD. When in 360 the Arians Aetius and Eunomius maintained the difference in essences between the Father and the Son and the created nature of the Holy Spirit, the theologians of Nicaean orthodoxy were challenged to develop a theory of the Homousia of the Father, Son and Holy Ghost which paved the way to the Trinitarian doctrinal decisions of the Council of Constantinople in 381.The two books Adversus Eunomium IV-V probably form the first literary reaction to the Neo-Arians and set the tone for the further development of the debate. In the MSS in which they are transmitted they follow on from the three books by Basil of Caesarea against Eunomius, but have been seen since at least the 18th century as pseudepigraphical and were probably composed by Apolinarius of Laodicea. The introduction to the present work discusses questions of authorship, identifies opponents (not only Aetius and Eunomius but also Marcellus of Ankyra), demonstrates the hitherto often questioned integrity of the tract and establishes the date of composition of Book IV as 360 and of Book V as 362/3. It also makes particularly clear the influence of contemporary philosophy. The translation follows the improved Migne text of 1886, while the commentary elucidates the often difficult content and prepares the way for further research on the interweaving of the threads of theological debate in the second half of the fourth century.