This chapter is almost at odds with the rest of the book, being largely algebraic in nature; it is included in the book mostly because my school wanted to see some Precalculus-like material in MAT 103: so it may certainly be omitted at first reading, or possibly replaced by my more geometrical paper "Isometries come in circles". The four basic isometries of the plane (translation, reflection, rotation, glide reflection) are introduced in both geometrical and algebraic forms, with the geometry of each isometry naturally leading to a formula for it; students are exposed to the equivalency between the algebra and the pictures, which serve as a way of checking 'abstract' computations. No matrices or complex numbers are involved, not even when an algebraic classification of planar isometries is presented.

Most of the chapter is written in a student-friendly manner requiring minimal algebraic background or mathematical maturity, but section 1.5 and even parts of section 1.0 could be an unexpected challenge.