An introduction to multiple orthogonal polynomials and Hermite-Pad\'e approximation

We present a brief introduction to the theory of multiple orthogonal polynomials on the basis of known results for an important class of measures known as Nikishin systems. For type I and type II multiple orthogonal polynomials with respect to such systems of measures, we describe some of their most relevant properties regarding location and distribution of zeros as well as their weak and ratio asymptotic behavior.