The BESIII Experiment at the Beijing Electron Positron Collider (BEPC2) has accumulated the world's largest samples of e+e- collisions in the tau-charm region. Using a sample of 106 million psi(3686) decays, the branch fractions of psi(3686) -> gamma chi_c0, gamma chi_c1, gamma chi_c2 are determined to be (9.389 +- 0.014 +- 0.332)%, (9.905 +- 0.011 +- 0.353)%, and (9.621 +- 0.013 +- 0.272)%, respectively. The branching fraction and the angular distributions of J/psi and psi(3686) decays to Lambda anti-Lambda and Sigma^0 anti-Sigma^0 final states are measured. J/psi and psi(3686) decays to Sigma(1385)^0 anti-Sigma(1385)^0 and Xi^0 anti-Xi^0 are measured. The decays to Sigma(1385)^0 anti-Sigma(1385)^0 are observed for the first time, and the angular parameters of these decays are also measured first time. Observation of hc radiative decay hc -> gamma eta' and evidence for hc -> gamma eta. The branching fractions are measured to be (1.52 +- 0.27 +- 0.29)/10^3 and (4.7 +- 1.5 +- 1.4)/10^4, respectively. Both of them are the first observations. Measurement of higher-order multipile amplitudes in psi(3686) -> gamma chi_c1,2 with chi_c1,2 -> gamma J/psi and search for the eta_c(2S) -> gamma J/psi transition. The normalized magnetic-quadrupole (M2) amplitude for psi(3686) -> gamma chi_c1,2 -> gamma gamma J/psi and the normalized electricoctupole (E3) amplitudes for psi(3686) -> gamma chi_c2, chi_c2-> gamma J/psi are determined. The decays psi(3686) -> e+ e- chi_c0,1,2 and chi_c0,1,2 -> e+ e-J/psi are searched, and they are observed for the first time. Improved measurements of branching fractions for eta_c -> phi phi and omega phi. The branching fraction of eta_c -> phi phi is measured with improved precision. No significant signal for the double OZI-suppressed decay of eta_c -> omega phi is observed, and the upper limit on the branching fraction is determined.