'This book provides a short and easy-to-read account of the theory of Gröbner bases and its applications.' L'Enseignment Mathématique

• Preface; 1. Programme committee; Introduction to Gröbner bases B. Buchberger; 2. Gröbner bases, symbolic summation and symbolic integration F. Chyzak; 3. Gröbner bases and invariant theory W. Decker and T. de Jong; 4. Gröbner bases and generic monomial ideals M. Green and M. Stillman; 5. Gröbner bases and algebraic geometry G. M. Greuel; 6. Gröbner bases and integer programming S. Hosten and R. Thomas; 7. Gröbner bases and numerical analysis H. M. Möller; 8. Gröbner bases and statistics L. Robbiano; 9. Gröbner bases and coding theory S. Sakata; 10. Janet bases for symmetry groups F. Schwarz; 11. Gröbner bases in partial differential equations D. Struppa; 12. Gröbner bases and hypergeometric functions B. Sturmfels and N. Takayama; 13. Introduction to noncommutative Gröbner bases theory V. Ufnarovski; 14. Gröbner bases applied to geometric theorem proving and discovering D. Wang; 15. The fractal walk B. Amrhein and O. Gloor; 16. Gröbner bases property on elimination ideal in the noncommutative case M. A. Borges and M. Borges; 17. The CoCoA 3 framework for a family of Buchberger-like algorithms A. Capani and G. Niesi; 18. Newton identities in the multivariate case: Pham systems M.-J. González-López and L. González-Vega; 19. Gröbner bases in rings of differential operators M. Insa and F. Pauer; 20. Canonical curves and the Petri scheme J. B. Little; 21. The Buchberger algorithm as a tool for ideal theory of polynomial rings in constructive mathematics H. Lombardi and H. Perdry; 22. Gröbner bases in non-commutative reduction rings K. Madlener and B. Reinert; 23. Effective algorithms for intrinsically computing SAGBI-Gröbner bases in a polynomial ring over a field J. L. Miller; 24. De Nugis Groebnerialium 1: Eagon, Northcott, Gröbner F. Mora; 25. An application of Gröbner bases to the decomposition of rational mappings J. Müller-Quade, R. Steinwandt and T. Beth; 26. On some basic applications of Gröbner bases in noncommutative polynomial rings P. Nordbeck; 27. Full factorial designs and distracted fractions L. Robbiano and M. P. Rogantin; 28. Polynomial interpolation of minimal degree and Gröbner bases T. Sauer; 29. Inversion of birational maps with Gröbner bases J. Schicho; 30. Reverse lexicographic initial ideas of generic ideals are finitely generated J. Snellman; 31. Parallel computation and Gröbner bases: an application for converting bases with the Gröbner walk Q.-N. Trân; 32. Appendix. an algorithmic criterion for the solvability of a system of algebraic equations B. Buchberger (translated by M. Abramson and R. Lumbert); Index of Tutorials.