Numerical Methods for Hyperbolic Equations is a collection of 49 articles presented at the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications (Santiago de Compostela, Spain, 4-8 July 2011). The conference was organized to honour Professor Eleuterio Toro in the month of his 65th birthday. The topics covered include: * Recent advances in the numerical computation of environmental conservation laws with source terms * Multiphase flow and porous media * Numerical methods in astrophysics * Seismology and geophysics modelling * High order methods for hyperbolic conservation laws * Numerical methods for reactive flows * Finite volume and discontinous Galerkin schemes for stiff source term problems * Methods and models for biomedical problems * Numerical methods for reactive flows The research interest of Eleuterio Toro, born in Chile on 16th July 1946, is reflected in Numerical Methods for Hyperbolic Equations, and focuses on: numerical methods for partial differential equations, with particular emphasis on methods for hyperbolic equations; design and application of new algorithms; hyperbolic partial differential equations as mathematical models of various types of processes; mathematical modelling and simulation of physico/chemical processes that include wave propagation phenomena; modelling of multiphase flows; application of models and methods to real problems. Eleuterio Toro received several honours and distinctions, including the honorary title OBE from Queen Elizabeth II (Buckingham Palace, London 2000); Distinguished Citizen of the City of Carahue (Chile, 2001); Life Fellow, Claire Hall, University of Cambridge (UK, 2003); Fellow of the Indian Society for Shock Wave Research (Bangalore, 2005); Doctor Honoris Causa (Universidad de Santiago de Chile, 2008); William Penney Fellow, University of Cambridge (UK, 2010); Doctor Honoris Causa (Universidad de la Frontera, Chile, 2012). Professor Toro is author of two books, editor of two books and author of more than 260 research works. In the last ten years he has been invited and keynote speaker in more than 100 scientific events. Professor Toro has held many visiting appointments round the world, which include several European countries, Japan, China and USA.