This book constitutes the refereed proceedings of the Third International Workshop on the Theory and Applications of Formal Argumentation, TAFA 2015, held in Buenos Aires, Argentina, in July 2015. The workshop was co-located with IJCAI 2015. The 15 revised full papers presented were carefully reviewed and selected from 25 submissions. The papers deal with formal theoretical models of argumentation and application of such models in subfields of AI, evaluation of models, both theoretical and practical, and theories and applications developed through inter-disciplinary collaboration. .