This leads to di?culties in that, although many of the elementary properties of ?nite-dimensional vector spaces hold in in?nite-dimensional vector spaces, many others do not. Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space.

Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory. Written in an informal style, the material is divided into short sections each of which deals with an important result or a new idea.

Throughout the book, the emphasis is placed on concrete examples, many of them geometrical in nature, so that finite rotation groups and the seventeen wallpaper groups are tr...