Multiple orthogonal polynomials of two real variables

Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Padé approximation, random matrix theory or integrable systems. However, this theory has only been studied in the univariate case. In this paper, we present an introduction to Multiple Orthogonality in one variable and its main properties, followed by some generalized definitions of the two main types of multiple orthogonality, together with some examples and extended results.