This volume comprises a collection of invited papers presented at the international symposium "The Future of Muon Physics", May 7-9 1991, at the Ruprecht­ Karls-Universitat in Heidelberg. In the inspiring atmosphere of the Internationales Wissenschaftsforum researchers working worldwide at universities and at many inter­ national accelerator centers came together to review the present status of the field and to discuss the future directions in muon physics. The muon, charged lepton of the second generation, was first oberved some sixty years ago~ Despite many efforts since, the reason for its existence still remains a secret to the scientific community challenging both theorists and experimentalists. In modern physics the muon plays a key role in many topics of research. Atomic physics with negative muons provides excellent tests of the theory of quantum electrodynamics and of the electro-weak interaction and probes nuclear properties. The. purely leptonic hydrogen-like muonium atom allows tests of fundamental laws in physics and the determination of precise values for fundamental constants. New measurements of the anomalous magnetic moment of the muon will probe the renormalizability of the weak interaction and will be sensitive to physics beyond the standard model. The muon decay is the most carefully studied weak process. Searches for rare decay modes of muons and for the conversion of muonium to antimuonium examine the lepton number conservation laws and new speculative theories. Nuclear muon capture addresses fundamental questions like tests of the CPT theorem.