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We present the theory and the analytical and numerical solution for the calculation of the oscillator and rotatory strengths of molecular systems using a state-specific formalism. For a start, this is done in the context of the exact semiclassical light–matter interaction in association with electronic wave functions expanded in a Gaussian basis. The reader is guided through the standard approximations of the field, e.g., the use of commutators, truncation of Taylor expansions, and the implications of these are discussed in parallel. Expressions for the isotropically averaged values are derived, recovering the isotropic oscillator strength in terms of the transition electric-dipole moment, and the isotropic rotatory strength in terms of the transition electric-dipole and magnetic-dipole moments. This chapter gives a detailed description of the computation of the integrals over the plane wave in association with Gaussian one-particle basis sets. Finally, a brief description is given of how the computed oscillator and rotatory strengths are related to the quantities commonly used and discussed in experimental studies., QC 20200402