A text for undergraduates on developing abstract algebraic techniques. It refers to the famous problems of squaring the circle, doubling the cube and trisecting the angle which did not yield to geometric solution and whose intrinsic impossibility was discovered by abstract algebra.

The famous problems of squaring the circle, doubling the cube, and trisecting the angle have captured the imagination of both professional and amateur mathematician for over 2000 years. These problems, however, have not yielded to purely geometrical methods. It was only the development of abstract algebra in the 19th century which enabled mathematicians to arrive at the surprising conclusion that these constructions are not possible. This text aims to develop the abstract algebra.