This volume brings together innovative contributions to the question of the spatial turn. While the spatial turn refers to the production of space through social practices, the embedding of these practices in technical systems has been overlooked. Given our lives in technified spaces, this gap is acute. This complex was explored in a research project titled "Topology of Technology," the results of which are documented in the Topological Manifesto. In this volume, alongside the manifesto, contributions from various disciplines are gathered to explore the possibilities and limitations of a topology of technology. Starting from a modal concept of power, the inquiry addresses the technogenic formation and transformation of spaces, the conceptualization of relational spaces as structure or network, and the role of imagination in space-forming processes.