This entry is about the notion of lattice in group theory/quadratic form-theory. For other notions see at lattice (disambiguation).
A lattice in the Cartesian space $\mathbb{R}^n$ is a discrete subgroup (of the underlying topological abelian group) that spans $\mathbb{R}^n$ as a vector space over $\mathbb{R}$.
A. E. Brouwer, Lattices, Course notes (2002) (pdf)
John Conway, N. Sloane, Low dimensional lattices I: Quadratic forms of small determinant
Wikipedia, Lattice (group)
Wikipedia, Lattice (module)