  This is an introduction to the theory of normal bases of finite fields. The
first few chapters cover a wide range of topics on the theory of normal bases
of finite fields. Most standard definitions and results, including proofs are
given. The last few chapters cover the theory of guassian and period normal
bases of finite fields of low degrees. The last chapter presents the asymptotic
proofs of the existence of primitive polynomials of degree n with approximately
n/2 arbitrary coefficients, and primitive normal polynomials of arbitrary
traces.
