The target audience for this point set topology textbook is upper-undergraduate students. Students who are still learning how to write proofs can benefit from its patient pace. Calculus and at least one semester of analysis are prerequisites, with the latter ensuring that the student has had an adequate introduction to concepts from basic set theory, such as subsets, unions, intersections, and functions, as well as convergence and other topological principles in the real line. To fill the gap between this new material and the content contained in an analytical course, appendices are provided. Metric spaces are one of the topological spaces that are utilised more frequently in other fields, hence this text emphasises them throughout and introduces them in the first chapter. Additionally, this is consistent with the book's method of start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.