In this chapter, we give an overview over the basic concepts of logarithmic geometry used in this monograph. We review monoids, ideals, and faces as well as some of their properties. We discuss integral, saturated, and vertical monoid homomorphisms. We then discuss log schemes and their basic constructions as well as charts and coherence. We review the log de Rham complex and log smoothness. We then discuss Fumiharu Kato’s log smooth deformation theory, which is a model for the more general logarithmic deformation theory in this monograph. We conclude the chapter with Tsuji’s isomorphism between the log canonical sheaf and the dualizing sheaf in certain cases. The chapter can be used as a starting point to learn logarithmic geometry and contains a guide to read Ogus’ book on the foundations thereof.