  This is the Foreword to the book ``Explicit birational geometry of 3-folds'',
edited by A. Corti and M. Reid, CUP Jun 2000, ISBN: 0 521 63641 8, with papers
by K. Altmann, A. Corti, A.R. Iano-Fletcher, J. Koll\'ar, A.V. Pukhlikov and M.
Reid.
  One of the main achievements of algebraic geometry over the last 20 years is
the work of Mori and others extending minimal models and the Enriques--Kodaira
classification to 3-folds. This book is an integrated suite of papers centred
around applications of Mori theory to birational geometry. Four of the papers
(those by Pukhlikov, Fletcher, Corti, and the long joint paper Corti, Pukhlikov
and Reid) work out in detail the theory of birational rigidity of Fano 3-folds;
these contributions work for the first time with a representative class of Fano
varieties, 3-fold hypersurfaces in weighted projective space, and include an
attractive introductory treatment and a wealth of detailed computation of
special cases.
