This book is about the branch of mathematics called topology.But its larger purpose is to illustrate how mathematics works: The interplay between intuition on the one hand and a puremathematical formulation on the other. Thus, we develop theaxioms for a topological space, formulate definitions withinthe context of those axioms and actually prove theorems fromthe axioms. But underlying all this is our intuition abouttopology. It is this intuition that guides and gives "meaning" tothe definitions we make and to the theorems we prove. No priorknowledge of mathematics is assumed. In fact, these wereoriginally the notes for a course for freshman non-scientists.This book, including over 100 figures and problem sets withsolutions, should be of interest to those who would like tounderstand what mathematics is all about, as well as thosewho would like to learn about the this important branch ofmathematics.