The concept is introduced in Chapter 3 of [Choset], Chapter 2 of [Latombe], Chapter 4 of [LaValle]. The level of mathematical treatment, and the number of examples, varies considerably among these references.
An introductory-level presentation of SO(n) and SE(n) is given in Chap. 2 of [SHV].
A treatment of SO(n) as a manifold is given in Chap. 2 of [Latombe].
A general treatment, including exponential coordinates for rotation, is given in Chap. 2 of [MLS].
An introduction to SO(2) and SO(3), along with some nice examples, is given in Chapter 3 of [LaValle].