In this chapter, we fix our definitions of some algebraic structures. Concretely, these are Lie algebras, Lie–Rinehart algebras, Lie–Rinehart pairs, Gerstenhaber algebras, Batalin–Vilkovisky algebras, Gerstenhaber calculi, and Batalin–Vilkovisky calculi. They all come in a plain version, a graded or bigraded version, and a curved version. The relevant examples in logarithmic deformation theory are given by the log de Rham complex and the log polyvector fields, along with acyclic resolutions thereof. The role of these structures in logarithmic deformation theory is given by the fact that the logarithmic Bogomolov–Tian–Todorov theorem is proven by demonstrating an abstract unobstructedness theorem for curved Batalin–Vilkovisky algebras and curved Batalin–Vilkovisky calculi.