These notes were written for a final year undergraduate course taught at Manchester University
in 1988/9 and also taught in later years by Dr M. McCrudden. I rewrote them in 2000 to
make them available to interested graduate students. The approach taken is very down to earth
and makes few assumptions beyond standard undergraduate analysis and algebra. Because of
this the course was as self contained as possible, covering basic number theory and analytic
ideas which would probably be familiar to more advanced readers. The problem sets are based
on those for produced for the course.