In this article we present diverse experiences of Polish mathematicians (in a broad sense) who during World War I fought for freedom of their homeland or conducted their research and teaching in difficult wartime circumstances. We discuss not only individual fates, but also organizational efforts of many kinds (teaching at the academic level outside traditional institutions, Polish scientific societies, publishing activities) in order to illustrate the formation of modern Polish mathematical community.In Part I we focus on mathematicians affiliated with the existing Polish institutions of higher education: Universities in Lwów in Kraków and the Polytechnical School in Lwów, within the Austro-Hungarian empire.W niniejszym artykule przedstawi...