Designed for junior-senior level mathematics majors, including those who plan to teach secondary mathematics. Chapters include lists of suggested sources for applications and/or related topics in areas such as art and history.

*Chapter 1*describes axiomatic systems and presents finite geometry examples.*Chapter 2*explores Euclid's geometry and basic ideas of non-Euclidean geometry with special emphasis on hyperbolic geometry.*Chapter 3*introduces symmetry and isometries via hands-on explorations, and then formally presents transformations of the Euclidean plane, using matrix representations.*Chapter 4*presents plane projective geometry first synthetically, and then analytically by generalizing the transformation coverage of Chapter 3.*Chapter 5*explores chaos theory and fractal geometry, stressing the self-similar nature of fractals and the role of transformations from Chapter 3 in their generation.

**A. Errata for Second Edition **

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