This part of the BETL documentation serves as an introduction to Boundary Element Methods — in particular it is meant to be an introduction to symmetric Galerkin-based three-dimensional Boundary Element Methods. Naturally, this introduction is neither a comprehensive treatise on Boundary Integral Equations nor gives it an detailed overview on their respective discretisation schemes, the Boundary Element Methods. For this the reader is referred to well-known literature like, e.g., [GlEtAl03], [Hckbsch89], [HsWdlnd08], [McLn00], [StrSchwb11], [Stnbch08], [StrdhrEtAl08]. This introductory chapter is basically about the definition of a common language. Hence, even if you are familiar with Boundary Element Methods (and we assume that you are!) at least a rough reading through this chapter is recommended since it may help to clarify the notion of expressions.