  In this paper we discuss about properties of lattices and its application in
theoretical and algorithmic number theory. This result of Minkowski regarding
the lattices initiated the subject of Geometry of Numbers, which uses geometry
to study the properties of algebraic numbers. It has application on various
other fields of mathematics especially the study of Diophantine equations,
analysis of functional analysis etc. This paper will review all the major
developments that have occurred in the field of geometry of numbers. In this
paper we shall first give a broad overview of the concept of lattice and then
discuss about the geometrical properties it has and its applications.
