This book constitutes the refereed proceedings of the Second International Joint Conference on Automated Reasoning, IJCAR 2004, held in Cork, Ireland, in July 2004. IJCAR 2004 comprises CADE, CALCULEMUS, FroCoS, FTP, and TABLEAUX.The 26 revised full research papers and 6 revised system demonstrations presented together with 3 invited papers and a summary of a systems competition were carefully reviewed and selected from a total of 86 submissions. The papers are organized in topical sections on rewriting, saturation-based theorem proving, combination techniques, verification and systems, reasoning with finite structure, tableaux and non-classical logics, applications and systems, computer mathematics, interactive theorem proving, combinatorial reasoning, and higher-order reasoning.