Chapter Eighteen. Topological Theories of Social Choice This chapter presents a simple introduction to the main results in topological social choice theory. Given a continuous social welfare function these results show the following: (i) Unanimity and Anonymity are incompatible; (ii) Weak Pareto and No Veto are incompatible; and (iii) Weak Pareto implies the existence of a Strategic Manipulator. Given the role of continuity in all these results its justification is critically discussed. Finally a remarkable proof of Arrows theorem using topological methods is presented.