We begin Chapter I by developing in a concise but complete fashion the basic concepts of group theory (§1–§4). These sections contain numerous elementary theorems and lemmas that will be used repeatedly later on; this applies in particular to the product formula in Lemma 2.12 a), the Dedekind identity in Lemma 2.12 c), Lemma 2.13 and Theorems 4.5, 4.8 and 4.9. The representations of a group as a permutation group (§6) yield the fundamental Sylow theorems (§7) as an important consequence. Several elementary criteria for solvability will be deduced from Sylow’s theorems in §8.