This volume presents lively and engaging articles from the lecturers and the participants of the 25th and 26th Goekova Geometry-Topology Conferences, held on the shores of Goekova Bay, Turkey, in May/June of 2018 and May/June of 2019. The 25th and 26th Goekova Geometry-Topology Conferences were sponsored by the National Science Foundation, by the Turkish Mathematical Society, and by the European Research Council.