This paper introduces a special issue of the journal on the subject of Project Varenius, a three-year effort funded by the US National Science Foundation to advance geographical information science. Geographical information is first defined as an abstraction of primitive tuples linking geographical locations to general descriptors. Geographical concepts originate in the human mind, and are instantiated in geographical information. Geographical information technologies apply digital methods to geographical information. Finally, geographical information science is defined as the set of basic research issues arising from these technologies. Three motivations are presented for research in this area: scientific, technological, and societal. Within the project, geographical information science is structured by a three-part framework that includes cognitive, computational, and societal issues. The paper ends with an introduction to these three parts, which define the infrastructure of the project and are discussed at length by the subsequent three papers.