This book presents Hyper-lattice, a new algebraic model for partially ordered sets, and an alternative to lattice. The authors analyze some of the shortcomings of conventional lattice structure and propose a novel algebraic structure in the form of Hyper-lattice to overcome problems with lattice. They establish how Hyper-lattice supports dynamic insertion of elements in a partial order set with a partial hierarchy between the set members. The authors present the characteristics and the different properties, showing how propositions and lemmas formalize Hyper-lattice as a new algebraic structure. © The Author(s) 2016. All rights reserved.