Sheldon Davis' text is written for introductory courses in topology taken by advanced undergraduate and beginning graduate students. Designed to be... flexible, the text is divided into two parts to accomodate different courses, course configurations, and instructor preferences. Part I of the text covers the bare essentials every student should know about topology before continuing on to study point-set or set-theoretic topology, algebraic topology, funcitonal analysis, continuum theory, or the many other important areas in mathematics that utilize topology fundamentals. To keep the text manageable for beginning students, use of set theory in Part I is kept to an intuitive level. Part II contains a complete beginning course in general topology, or set-theoretic topology. General topology courses that assume prior background in the fundamentals can start directly with Part II and use the material in Part I for conceptual review. This text is part of the Walter Rudin Student Series in Advanced Mathematics.