In the last chapter, we established the fundamental principles for bipartite entanglement. Moving forward, this chapter marks the beginning of our exploration into more complicated quantum systems. Specifically, we will study “genuine” multipartite entanglement. We will first identify known challenges due to insufficient recognition of the role of multipartite entanglement in practical problems. Subsequently, we introduce the notion of “qubit power” within multi-party systems, which leads to the concept of “genuine multipartite entanglement.” Following this, we will explore the classifications of entanglement in multi-party systems, for both pure-state systems and mixed-state systems. To conclude, we will introduce several existing measures to quantify genuine multipartite entanglement, all using algebraic approaches.