This chapter provides an introduction to the fundamental concepts on numerical semigroups and their semigroup rings. Symmetric numerical semigroups and the gluing construction, which is a method for building new symmetric numerical semigroups from existing ones are considered. The semigroup ring of a numerical semigroup is introduced and its defining ideal is described. The algebraic structure of this ring very well reflects and explains in many cases properties of the underlying numerical semigroup. Special attention is given to relations for families of numerical semigroups, including those arising from gluing, complete intersections, and 3-generated cases. We close the chapter with the study of numerical semigroups of maximal embedding dimension.