Introduction: Reflection groups and invariant theory

The concept of a reflection group is easy to explain. A reflection in Euclidean space is a linear transformation of the space that fixes a hyperplane while sending its orthogonal vectors to their negatives. A reflection group is, then, any group of transformations generated by such reflections. The purpose of this book is to study such groups and their associated invariant theory, outlining the deep and elegant theory that they possess.