Topology, one of the speaker's main research interests, is the study of the properties of "shapes" and "spaces." Ideas and methods of solving problems coming from topology are becoming more and more influential to all other branches of mathematics. More recently, the word "topological" has also starting to appear outside the mathematical world. One of the advantages of topological methods is that they provide a tool to turn some geometric data into some algebraic ones such as groups. In this talk, the speaker would like to give the audience some ideas on how one might think as a topologist through concrete examples. The speaker will also mention some related topics motivated by a current project on combinatorial reconfiguration.