  This article is based on lectures given by the authors in 2005 and 2006. Our
first goal is to present an introduction to the orbit method with an emphasis
on the character theory of finite nilpotent groups. The second goal (motivated
by a recent work of G. Lusztig) is to explain several nontrivial aspects of
character theory for finite groups of the form $G(F_{q^n})$, where $G$ is a
unipotent algebraic group over a finite field $F_q$. In particular, we
introduce the notion of a character sheaf for a unipotent group, and provide a
toy model for the representation-theoretic notion of an L-packet.
