**Counterexamples in Topology** is a book by Lynn Arthur Steen and J. Arthur Seebach, Jr., second edition. It is a collection of 143 examples in topology, designed to help students understand topological concepts through concrete illustrations. The book is intended for undergraduate and graduate students, as well as their teachers, and serves as both a reference and a supplement to standard textbooks. The authors emphasize that examples are crucial in topology, as they make abstract concepts more concrete and help students explore the literature. Each example is designed to clarify definitions, theorems, and methods of proof. The book includes a variety of examples, ranging from simple topologies like the discrete and indiscrete topologies to more complex ones such as the Sorgenfrey line, the Cantor set, and the Tychonoff plank. These examples are organized roughly by their relevance to the definitions in the first section, though the order does not necessarily reflect difficulty. The book also includes appendices with reference charts that help locate examples based on properties. A general reference chart provides a comprehensive cross-tabulation of examples with properties, aiding in quick identification of specific types of examples. The authors also provide a classification of examples by sophistication level, with elementary, intermediate, and advanced categories. The second edition includes corrections to errors in the first edition, updates on recent developments in topology, and a revised version of a paper on metrization theory. The book is also accompanied by a list of problems related to the examples, which can be used as exercises for students. The authors acknowledge the contributions of undergraduate students who helped develop many of the examples, and they thank Rebecca Langholz for her assistance in typing the manuscript. The book is a valuable resource for students and researchers in topology, offering a wealth of historically and mathematically significant examples that can be used to explore and understand topological concepts.**Counterexamples in Topology** is a book by Lynn Arthur Steen and J. Arthur Seebach, Jr., second edition. It is a collection of 143 examples in topology, designed to help students understand topological concepts through concrete illustrations. The book is intended for undergraduate and graduate students, as well as their teachers, and serves as both a reference and a supplement to standard textbooks. The authors emphasize that examples are crucial in topology, as they make abstract concepts more concrete and help students explore the literature. Each example is designed to clarify definitions, theorems, and methods of proof. The book includes a variety of examples, ranging from simple topologies like the discrete and indiscrete topologies to more complex ones such as the Sorgenfrey line, the Cantor set, and the Tychonoff plank. These examples are organized roughly by their relevance to the definitions in the first section, though the order does not necessarily reflect difficulty. The book also includes appendices with reference charts that help locate examples based on properties. A general reference chart provides a comprehensive cross-tabulation of examples with properties, aiding in quick identification of specific types of examples. The authors also provide a classification of examples by sophistication level, with elementary, intermediate, and advanced categories. The second edition includes corrections to errors in the first edition, updates on recent developments in topology, and a revised version of a paper on metrization theory. The book is also accompanied by a list of problems related to the examples, which can be used as exercises for students. The authors acknowledge the contributions of undergraduate students who helped develop many of the examples, and they thank Rebecca Langholz for her assistance in typing the manuscript. The book is a valuable resource for students and researchers in topology, offering a wealth of historically and mathematically significant examples that can be used to explore and understand topological concepts.