The main aim of the thesis is to explore the structure of the world from a Whiteheadian process theoretic perspective and suggest it as a framework for an algebraic approach to Quantum Gravity. In particular, throughout the thesis, the analysis focuses on the notion of dipolarity that appears in Whitehead’s philosophy. The thesis begins with an exploration of Whitehead’s process of becoming which is followed by a presentation of sheaf theory as the mathematical basis. Based on the analysis of Whitehead’s philosophy in combination with physical theories, the features of the structure of the world are explored. The process of becoming is translated as a transformation from determinable dispositions to determinate manifestations. In virtue of dispositions, the structure of the world acquires a causal status. The introduction of causality in terms of becoming is accompanied by the introduction of relata in the structure of the world. There is then a comparison between our Neo-Whiteheadian thesis and both structuralism and constructivism. In particular, the comparison with constructivism is justified by the fact that we adopt a view about the generation of abstract notions out of concrete instances or manifestations of determinable dispositions, where manifested quantities are related mereologically. On the other hand, the comparison with structuralism is motivated by the holistic character of the process of becoming. The thesis ends with exploring laws and the process notion of dipolarity.