Higher rank numerical ranges of normal operators

Research in higher rank numerical ranges has originally been motivated by problems in quantum information theory. The higher rank numerical range generalizes the classical numerical range of an operator. In this thesis, we present the basic structure and theory of higher-rank numerical ranges for unitary and normal operators and discuss some of their interesting geometric properties. We also introduce a general program to describe normal compressions of normal (diagonal) operators and discuss an interesting pair matching problem related to 2 x 2 compressions.