The current volume makes available a record of the expository and survey talks and a computational workshop in the International conference on Commutative Algebra and Combinatorics, organised by the Bhaskaracharya Pratishthana, Pune, and the Harish-Chandra Research Institute, in Allahabad just before the joint India-AMS Mathematics meeting in Bangalore, in December 2003. The 5 survey articles and the extended tutorial using Macaulay 2 and other software packages cover a remarkable range of current computational commutative algebra and algebraic geometry.
The central objects of study could be described with only the slightest oversimplification as ideals of monomials (Stanley-Reisner Theory) and rings generated by monomials (Toric Geometry). There is a clear description of the basic problems and constructions of current interest, as well as some of the major applications of this theory, from the enumeration of "magic squares" to algebraic statistics. Throughout there are plenty of open problems to orient newcomers to the area to the exciting work that is- and will be!- going on. I think that these expositions and surveys will be useful to any student (and lots of mature mathematicians) interested in aspects of these fields.
Summary by David Eisenbud