Part 1 : Universes. An introduction to the shape of the universe --
Visualizing four dimensions --
Geometry and topology of different universes --
Orientability --
Flat manifolds --
Connected sums of spaces --
Products of spaces --
Geometries of surfaces --
Part 2 : Knots. Introduction to knot theory --
Invariants of knots and links --
Knot polynomials --
Part 3 : Molecules. Mirror image symmetry from different viewpoints --
Techniques to prove topological chirality --
The topology and geometry of DNA --
The topology of proteins.

This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook. The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material