Filling functions Tim Riley Notes for a workshop on the Geometry of the Word Problem at the Centre de Recerca Matemàtica, Barcelona in July, 2005 Published as Part II of The Geometry of the Word Problem for Finitely Generated Groups, Advanced Courses in Mathematics CRM Barcelona, Birkhäuser-Verlag, 2007 Noel Brady and Hamish Short authored the other two parts. A preliminary version can be downloaded here (68 pages, 19 figures).