An integer lattice is a mathematical structure formed by points in space where each coordinate is an integer. In two dimensions, it consists of all points (x, y) where both x and y are whole numbers. This creates a grid-like pattern that extends infinitely in all directions. In higher dimensions, an integer lattice includes points (x_1, x_2, \ldots, x_n) where each x_i is an integer. Integer lattices are important in various fields, including number theory, geometry, and cryptography, as they help in understanding the properties of numbers and shapes in a structured way.