William P. Thurston's "The Geometry and Topology of Three-Manifolds" is an electronic edition of notes from 1980, originally distributed by Princeton University. The text was typed in TeX by Sheila Newbery and scanned, with some typos corrected. The book is a significant expansion of the first few chapters of these notes, while later chapters have not yet been published. The notes are based on a 1978–79 course at Princeton, with contributions from Bill Floyd, Steve Kerckhoff, and John Milnor. The goal is to explore the deep connection between geometry and low-dimensional topology, particularly for 3-manifolds and Kleinian groups. The material is new and challenging, requiring effort to understand. The notes are intended for graduate students and mathematicians in related fields. The contents include chapters on geometry and three-manifolds, elliptic and hyperbolic geometry, geometric structures on manifolds, hyperbolic Dehn surgery, flexibility and rigidity of geometric structures, Gromov's invariant, Kleinian groups, algebraic convergence, and orbifolds. The notes aim to provide a systematic understanding of three-manifolds, highlighting their rich geometric and topological properties. The text includes examples, diagrams, and references to illustrate complex concepts, emphasizing the importance of systematic approaches in studying three-manifolds.William P. Thurston's "The Geometry and Topology of Three-Manifolds" is an electronic edition of notes from 1980, originally distributed by Princeton University. The text was typed in TeX by Sheila Newbery and scanned, with some typos corrected. The book is a significant expansion of the first few chapters of these notes, while later chapters have not yet been published. The notes are based on a 1978–79 course at Princeton, with contributions from Bill Floyd, Steve Kerckhoff, and John Milnor. The goal is to explore the deep connection between geometry and low-dimensional topology, particularly for 3-manifolds and Kleinian groups. The material is new and challenging, requiring effort to understand. The notes are intended for graduate students and mathematicians in related fields. The contents include chapters on geometry and three-manifolds, elliptic and hyperbolic geometry, geometric structures on manifolds, hyperbolic Dehn surgery, flexibility and rigidity of geometric structures, Gromov's invariant, Kleinian groups, algebraic convergence, and orbifolds. The notes aim to provide a systematic understanding of three-manifolds, highlighting their rich geometric and topological properties. The text includes examples, diagrams, and references to illustrate complex concepts, emphasizing the importance of systematic approaches in studying three-manifolds.