This book covers most of the known results on reducibility of
polynomials over arbitrary fields, algebraically closed fields and
finitely generated fields. Results valid only over finite fields,
local fields or the rational field are not covered here, but
several theorems on reducibility of polynomials over number fields
that are either totally real or complex multiplication fields are
included. Some of these results are based on recent work of E.
Bombieri and U. Zannier (presented here by Zannier in an appendix).
The book also treats other subjects like Ritt's theory of
composition of polynomials, and properties of the Mahler measure,
and it concludes with a bibliography of over 300 items. This unique
work will be a necessary resource for all number theorists and
researchers in related fields.
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