Topics in Noncommutative Algebra. The Theorem of Campbell, Baker, Hausdorff and Dynkin.

This book is intended to present in a unified and self-contained way the natural context where the Campbell, Baker, Hausdorff, Dynkin Theorem (CBHD) can be formulated and proved. This context is of purely algebraic nature, but the proofs are very rich and diversified. Also, in order to understand and appreciate the variegated arguments attacking the proof of the CBHD Theorem, a historical overview of its early proofs is also given, without forgetting to catch a glimpse of more modern studies related to it, the state-of-the-art and some open problem. Most importantly, the aim is to look ahead to the applications of the CBHD Theorem. In order to point to these applications, it is first necessary to deal with the statements/proofs of the CBHD Theorem in the domain of Algebra, whereas the applications in Geometry and in Analysis eventually branch off from this algebraic setting. The book contains 10 Chapters and 2 Parts.