Summary: We point out many fields of mathematical social sciences where lattices are present, for instance the discrete resources allocation problems. However, we do not intend to survey the use of lattice theory in such discrete problems. Rather, we present an overview on the ubiquity and polymorphism of finite lattice theory, which accounts for its presence in these problems (like in many others). Indeed, on one hand lattices are on the border of two fundamental mathematical structures, namely algebra and order, and on the other hand they are naturally induced by several other significant mathematical objects like set systems, operators, binary relations or implications. We set out these different aspects and we illustrate them in the case of two significant classes of lattices, the lower locally distributive lattices and the distributive lattices.