The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) was held from June 29 July 3, 2010, in Uppsala, Sweden. This was the eighth conference in a series of biannual meetings starting in Paris (1995). S- sequent conferences were organized in Heidelberg (1997), Jyvas kyla (1999), Ischia (2001), Prague (2003), Santiago de Compostela (2005), and Graz (2007). ENU- MATH 2009 attracted over 330 attendees to the scienti c programme, with ten invited speakers, one public lecture, 32 minisymposia, and more than 280 presen- tions. This volume contains a selection of papers by the invited speakers and from the minisymposia and the contributed sessions. The purpose of the conference was to create a forum for discussion and d- semination of recent results in numerical mathematics and new applications of computational methods. Many subjects were covered in the talks and a few of the topicsrepresentedin these proceedingswere discontinuousGalerkinmethods, nite elementmethodsindifferentapplications,methodsfor uid ow,electromagnetism, nancial engineering,structuralmechanics, optimalcontrol, andbiomechanics. The minisymposia listed below with their organizers also give an impression of how broad the scope of the conference was: Adaptivity for non-linearand non-smooth problems, part I & II, Ralf Kornhuber, Andreas Veeser Advanced techniques in radial basis function approximation for PDEs,partI & II, Natasha Flyer, Elisabeth Larsson Advances in numerical methods for non-Newtonian ?ows, part I & II, Erik Burman, Maxim Olshanskii, Stefan Turek Anisotropicadaptivemeshes:erroranalysisandapplications,partI&II,Thierry Coupez, Simona Perotto Asymptotic linear algebra, numerical methods, and applications, part I & II, Marco Donatelli, Stefano Serra-Capizzano Biomechanics, part I & II, Gerhard A.