Title of Paper: The rational homotopy Lie algebra of function spaces Author(s) Aniceto Murillo and Urtzi Buijs AMS Classification numbers 55P62 Addresses of Authors Departamento de Algebra, Geometria y Topologia Universidad de Malaga, AP. 59, 29080 Malaga SPAIN Email address of Authors aniceto@agt.cie.uma.es urtzi@agt.cie.uma.es Text of Abstract (try for 20 lines or less) We give a full an explicit description of the rational homotopy Lie algebra of function spaces (gree or pointed)