Abstract: A matrix is called totally nonnegative if each of its square submatrices has a nonnegative determinant. Such matrices arise in a variety of applications such as differential equations, chemistry, stochastic processes and more. Two examples of totally nonnegative matrices are the: Vandermonde Matrix \tHilbert Matrix We will discuss combinatorial and other interpretations of such matrices. Some familiarity with linear algebra will be helpful but not necessary.