Difference sets are of central interest in finite geometry and
design theory. One of the main techniques to investigate abelian
difference sets is a discrete version of the classical Fourier
transform (i.e., character theory) in connection with algebraic
number theory. This approach is described using only basic
knowledge of algebra and algebraic number theory. It contains not
only most of our present knowledge about abelian difference sets,
but also gives applications of character theory to projective
planes with quasiregular collineation groups. Therefore, the book
is of interest both to geometers and mathematicians working on
difference sets. Moreover, the Fourier transform is important in
more applied branches of discrete mathematics such as coding theory
and shift register sequences.
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