This thesis focuses on the challenge of characterizing multipartite entanglement. While the study of bipartite entanglement is well-documented in scientific literature, recognizing that entanglement can involve more than two parties--i.e. three or more parties---is crucial, as multipartite entanglement enables the completion of more complicated tasks in quantum information science. Previous discussions on entanglement, especially within scenarios such as information scrambling, primarily concentrated on bipartite entanglement, thus overlooking the rich landscape of multipartite entanglement. By involving more parties, multipartite entanglement exhibits a larger degree of nonlocality, significantly deepening our insights into the dynamical properties of quantum many-body systems, going far beyond what has been revealed through bipartite entanglement. Despite its long-recognized importance, a proper quantification of multipartite entanglement, along with the understanding of the "genuine multipartite entanglement" criterion, continues to pose substantial challenges. The work in this thesis reveals an unexpected connection between multipartite entanglement and the geometry of simplices. Specifically, we demonstrate that every three-qubit state can be associated with a triangle, with its area measuring the genuine tripartite entanglement within that state. Similarly, every four-qubit state can be associated with a tetrahedron, with its volume measuring the genuine quadripartite entanglement within that state. With these results, we embark on a geometric journey toward addressing the quantification problem of genuine multipartite entanglement, offering new perspectives on the complexity of even larger quantum many-body systems. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]