# Introduction to Groups and Geometries

- Online Text
- Bound printed copy
*(to appear January 2021)*

## Status update 11/4/2020

*The first edition draft is complete! Editing continues, with a
stable edition target date of early January 2021. Discussion is
welcome! Contact the author at lyons (at) lvc.edu.*

## About the Textbook

This free, online text is designed for a one-semester undergraduate mathematics
course that combines an introduction to group theory with an
introduction to modern geometries using the Kleinian paradigm.

The chapter on groups develops the basic vocabulary and theory of
groups and homomorphisms, culminating with group
actions. The chapter on geometry makes use of group symmetries to build
the basic theory of MÃ¶bius, hyperbolic, elliptic, and projective
geometries.

The text is designed for active engagement, with carefully
structured exercises throughout.

The text assumes prerequisite courses in calculus, linear algebra,
and experience with proof writing.

## About the Author

David W. Lyons is a professor of mathematics at Lebanon
Valley College in Annville, Pennsylvania, USA, where he has
taught and conducted research since 2000. Lyons works in
mathematical physics, leading a student-faculty research program
in quantum information science since 2002. For more information,
visit his academic website at the URL below.

quantum.lvc.edu/lyons