This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality. Arithmetic geometry can be more generally defined as the study of schemes of finite type over the spectrum of the ring of integers. Arithmetic geometry has also been defined as the application of the techniques of algebraic geometry to problems in number theory.