Introduction

In this chapter we introduce the main objects of study and describe their early history as well as some later developments. In Section 1.1 the most classical of these objects – set partitions – are introduced and first properties of the corresponding Stirling and Bell numbers are discussed. Several further results are mentioned which will be discussed in later chapters in detail (and from different angles). In Section 1.2 the early history of the formal theory of operational or symbolical calculus is described and several results mentioned. Furthermore, the connection to the physical theory of quantum mechanics is elucidated, thereby motivating the same structure from a physical point of view. In Section 1.3 the “abstract” Weyl algebra and some close relatives are introduced and some of the more recent developments mentioned. Finally, in Section 1.4, the content of the book is described in more detail.