Let $X$ be a finite set and let ${\mathcal F}$ be a family of subsets of $X$. The (usual) incidence matrix of ${\mathcal F}$ with respect to $X$ is a $(0,1)$-matrix whose columns are indexed by the elements of $X$, whose rows are indexed by the elements of ${\mathcal F}$, and the $(A, x)$ entry of the matrix is 1 if $x\in A$, 0 otherwise, where $A\in {\mathcal F}$ and $x\in X$. Higher incidence matrices are defined in a similar way except that the columns of these matrices are indexed by subsets of $X$ of fixed size greater than one. We will discuss properties of these matrices, and show how to use these matrices to prove theorems in extremal combinatorics. The talk should be understandable by any one with basic knowledge in linear algebra.