Polo Grillo Nicola  
   Ph.D. thesis "Algorithms Computing Grobner Bases and Syzygies" (PDF). A computational introduction to Grobner Basis Theory and its applications: polynomials, Laurent polynomials, syzygies, inverse FIR filter and unimodular matrix completion.
   http://digilander.libero.it/pologrillo/

Manfred Minimair  
   Seton Hall University. Computational algebra. Publications and presentations.
   http://minimair.org/

Linton, Steve  
   Director, Centre for Interdisciplinary Research in Computational Algebra, University of St. Andrews. Leads the international consortium developing GAP. Publications, software.
   http://www.dcs.st-and.ac.uk/~sal/

Robertson, Edmund  
   University of St Andrews. Computational group theory, computational semigroup theory and algebra in general. Papers, seminars, teaching material and software.
   http://turnbull.mcs.st-and.ac.uk/~edmund/

Huczynska, Sophie  
   University of St Andrews. Number theory and combinatorics; algebra and theoretical computer science. Publications and teaching material.
   http://www-groups.mcs.st-andrews.ac.uk/~sophieh/