• Explores the mathematical field of topology, giving a sense of the visual elements of the field, as well as the formal definition of continuity
• Discusses the important implications of topology, a major field of maths, for science more generally, especially physics
• Considers some of the eye-opening examples that led mathematicians to recognize a need for studying topology
• Pays homage to the historical people, problems, and surprises that propelled the growth of the field

                    
Topology, the mathematical study of the properties that are preserved through the deformations, twistings, and stretchings of objects, is an important area of modern mathematics. As broad and fundamental as algebra and geometry, its study has important implications for science more generally, especially physics. Most people will have encountered topology, even if they're not aware of it, through Möbius strips, and knot problems such as the trefoil knot.
                    
In this Very Short Introduction Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field.