Professor Dana Scott, Carnegie Mellon University, presents his Distinguished Lecture entitled "Geometry Without Points". Ever since the compilers of Euclid's Elements gave the "definitions" that "a point is that which has no part" and "a line is breadth-less length", philosophers and mathematicians have worried that the basic concepts of geometry are too abstract and too idealized. In the 20th century writers such as Husserl, Lesniewski, Whitehead, Tarski, Blumenthal, and von Neumann have proposed "pointless" approaches. A problem more recent authors have emphasized it that there are difficulties in having a rich theory of a part-whole relationship without atoms and providing both size and geometric dimension as part of the theory. In this lecture, a solution will be proposed using the Boolean algebra of measurable sets modulo null sets along with relations derived from the group of rigid motions in Euclidean n-space. (Joint work with Tamar Lando, Columbia University.) This lecture was recorded on Monday 23 June at the University of Edinburgh's Appleton Tower.