A systematic discussion of the plethora of 2D materials follows the ‘aufbau’ principle of the periodic table, which explains the existence of various families of chemically related 2D compounds treated in detail in the following chapters of the book. The introduction gives a brief overview of the types of bonding in two-dimensional (2D) space, including the periodicity of bonding behavior based on the number of valence electronsValence electrons and a definition of covalently bonded monolayers and van der Waals bonded few-layer assemblies of monolayers and their heterostructures. This chapter outlines important theoretical approaches, such as first-principles density functional theory, which often delivers the most accurate results; molecular dynamics simulations, which provide thermal stabilityThermal stability at finite temperatures; tight-binding theory that is partially based on chemical intuition; and empirical rules, allowing a deeper understanding of the nature of chemical bonding. The description of the mechanical stiffness and strength of the 2D networks is described by their 2D units because it is possible to measure these quantities and to compare the behavior of different monolayers based on these units. Enormous information is available on the fundamental electronic properties, especially those of semiconductors with direct or indirect band gaps. Of particular interest are unique 2D-based properties and exotic behavior such as topological effectsTopological effects, which derive from specific bonding types and structural arrangements with lower symmetry than in 3D lattices. Moreover, the introduction provides an overview of the various methods used for synthesisSynthesis and diagnosis of 2D materials and briefly covers the influence of defects on the intrinsic properties of monolayers.