There are two important sets of problems in the theory of solvable groups, which overlap and complement each other in many ways: 1) The “arithmetic” structure of the group. The object of study here is the construction of the group from its Sylow subgroups and Hall subgroups. 2) The “normal” structure of the group. In this direction, the focus is on the chief factors and the lattice of normal subgroups. The goal is to construct the group, in the sense of extension theory, from abelian or nilpotent groups. We plan to discuss the lattice of so-called subnormal subgroups (these are the elements in a composition series) in later volumes; this theory yields particularly sharp statements when some of the composition factors are nonsolvable. However, it has not made a substantial contribution to the theory of solvable groups at the time of writing.