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.