Geometry is the study of shapes and spaces.
In its modern form geometry has a much wider scope, reaching into higher dimensions and encompassing a broad range of current ideas. The subject of topology is concerned with those features of geometry which remain unchanged after twisting, stretching or other deformations of a geometrical space. It includes such problems as coloring maps, distinguishing knots and classifying surfaces and their higher dimensional analogs. History of Topology in the History of Mathematics archive at Saint Andrews University in Scotland. A Circular History of Knot Theory.