This book offers a new look at emergence in terms of a hierarchical emergent ontology. Emergence is recognised as a universal principle, as universal as the principle of evolution. This is achieved by setting out the ontological criteria of emergence and such criteria's various roles. The traditional dichotomies are overcome, e.g., the synchronic and diachronic perspectives are unified, allowing a single, universal principle of emergence to be applied across various fields of science. As exemplars of its practical utility in both explanation and prediction, this new approach is applied to three different scientific areas: cellular automata, quantum Hall effects, and the neural network of the mind. It proves that the resulting metaphysics of hierarchical emergent ontology plays a fundamental role in unifying science, an impossible task under classical reductionism.