Using a sample of 106 Â 10 6 c ð3686Þ events collected with the BESIII detector at the BEPCII storage ring, we have made the first measurement of the M1 transition between the radially excited charmonium S-wave spin-triplet and the radially excited S-wave spin-singlet states: c ð3686Þ ! c ð2SÞ. Analyses of the processes c ð3686Þ ! c ð2SÞ with c ð2SÞ ! K The quarkonium states play an important role in understanding the strong interaction between quarks. The charmonium states below the open-charm production threshold are relatively well understood, with the notable exception of the spin singlets [1], which include the P-wave state h c and the S-wave ground state c and its first radial excitation c ð2SÞ [2]. These are experimentally challenging because of the low production rates and spin-parity quantum numbers that are inaccessible in direct e þ e À annihilations. The c ð2SÞ was first observed by the Belle collaboration in the processIt was confirmed in the two-photon production of 6,7]. In this Letter, we report the first observation of c ð3686Þ ! c ð2SÞ,,5], and in the double-charmonium production process e þ e À ! J=c c " c [The data sample for this analysis consists of an integrated luminosity of 156 pb À1 (106 Â 10 6 events) produced at the peak of the c ð3686Þ resonance [17] and collected in the BESIII detector [18]. An additional 42 pb À1 of data were collected at a center-of-mass energy of ffiffi ffi s p ¼ 3:65 GeV to determine nonresonant continuum background contributions.The BESIII detector, described in detail in Ref. [18], has an effective geometrical acceptance of 93% of 4. A small-cell, helium-based main drift chamber in a 1-T magnetic field provides a charged-particle momentum resolution of 0.5% at 1 GeV=c, and specific-ionization (dE=dx) measurements for particle identification with a resolution better than 6% for electrons from Bhabha scattering. The cesium iodide electromagnetic calorimeter (EMC) measures photon energies with resolutions at 1.0 GeV of 2.5% and 5% in the detector's barrel (j cosj < 0:8, where is the polar angle with respect to the e þ direction) and end caps (0:86 < j cosj < 0:92), respectively. Additional particle identification is provided by a time-of-flight system with a time resolution of 80 ps (110 ps) for the barrel (end caps).Reconstructed charged tracks other than daughters of K