This work provides a lucid and rigorous account of the foundations
of algebraic geometry. The authors have confined themselves to
fundamental concepts and geometrical methods, and do not give
detailed developments of geometrical properties but geometrical
meaning has been emphasised throughout. Here in this volume, the
authors have again confined their attention to varieties defined on
a ground field without characteristic. In order to familiarize the
reader with the different techniques available to algebraic
geometers, they have not confined themselves to one method and on
occasion have deliberately used more advanced methods where
elementary ones would serve, when by so doing it has been possible
to illustrate the power of the more advanced techniques, such as
valuation theory. The other two volumes of Hodge and Pedoe's
classic work are also available. Together, these books give an
insight into algebraic geometry that is unique and unsurpassed.
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