The decay of the muon has been studied at PSI with several precision measurements: The longitudinal polarization P_{\mathrm{L}}(E) P L ( E ) with the muon decay parameters \xi' ξ ′ , \xi'' ξ ″ , the Time-Reversal Invariance (TRI) conserving transverse polarization P_{\mathrm{T_{1}}}(E) P T 1 ( E ) with the muon decay parameters \eta η , \eta'' η ″ , the TRI violating transverse polarization P_{\mathrm{T_{2}}}(E) P T 2 ( E ) , with \alpha'/A α ′ / A , \beta'/A β ′ / A and the muon decay asymmetry with P_{\mu}\xi P μ ξ . The detailed theoretical analysis of all measurements of normal and inverse muon decay has led for the first time to a lower limit |g^{V}_{LL}| > 0.960 | g L L V | > 0.960 (“ V-A V − A ”) and upper limits for nine other possible complex couplings, especially the scalar coupling |g^{S}_{LL}| < 0.550 | g L L S | < 0.550 which had not been excluded before.