This book has grown out of two courses the author has taught at the University at Albany. The first course investigates the rigid motions (isometries) of the Euclidean plane and develops rosette, frieze and wallpaper groups. In particular, we study discrete subgroups of the group of isometries of the plane (i.e., two-dimensional crystallographic groups).

• Some linear algebra
• Basic Euclidean geometry
• Groups
• Linear isometries
• Isometries of R^2
• Groups of symmetries: planar figures
• Linear isometries of R^3
• Spheres and other manifolds
• Spherical geometry
• Tangent bundles
• Riemannian manifolds
• Hyperbolic geometry
• Appendix A. Spaces with identifications

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