Quantum information theory studies the way information is stored, transmitted and processed in quantum devices. Mathematically, quantum information theory extends Shannon's theory of information but differs from it by allowing both for stronger correlations known as entanglement and for non-commutative effects resulting in measurement uncertainty as required by the laws of quantum physics. Entanglement has been shown to be crucial for the advantages offered by quantum communication and computation.In recent years, researchers have gained a good understanding of quantum information theory involving two parties, for instance in the transmission of quantum bits from a sender to a receiver. Yet the study of quantum protocols for communication tasks involving multiple parties, for instance the joint counting of online votes or the compression of data distributed in a network, is still in its infancy. The reason for this is two-fold: (i) a lack of understanding of entanglement among multiple particles and (ii) the non-commutative nature of quantum theory, two facts that pose major difficulties for the design of multiparty quantum coding schemes.It is the goal of this research project to overcome these two main obstacles so that a comprehensive theory of quantum information can be developed. Just as the Internet, where a network of many interacting computers has replaced point-to-point communication channels such as phone lines, the future of quantum communication will involve communication among many parties. The multipartite quantum information theory explored in this project is therefore expected to impact not only current experiments but also our future communication infrastructure.