A unimodular matrix is a matrix whose determinant is $\pm 1$. Often, but not always, its entries are integers.
An integer unimodular matrix is a matrix $M$ with $m_{ij}\in \mathbb{Z}$ and $\det(M)=\pm 1$. Note that upper and lower integer matrices with $1$ on the main diagonal, such as Pascal matrices, are unimodular. The unimodular matrices of a fixed dimension $n\times n$ form a group under matrix multiplication.
One generalization allows for the entries of $M$ to be in $F[x]$ for some field $F$ and then requiring the determinant to be a unit of $F[x]$, which implies the entries of $M^{-1}$ are in $F[x]$ as well.
A related concept is totally unimodular: a matrix $M$ is totally unimodular if every square submatrix has determinant $-1,0,1$.
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