By using the strong-field scheme, we have calculated all the reduced matrix elements and the matrix elements of the trigonal crystal field and all the matrix elements of the spinorbit interaction for the d 3 electronic configuration: The complete energy matrix of the d configuration in trigonal Held has been constructed. This matrix has been diagonalized to fit the experimental optical and microwave spectral data of ruby. The calculated results are in good agreement with the experimental data. In particular, the zero-field splitting S of the ground state and the splitting between Ri and R 2 lines agree very well with the experimental results. The assignments of all the energy levels and the rates of change of the levels with respect to various parameters are given. The contributions from various parameters to 6 and the splitting between R\ and R 2 lines are aiso giveji.