The qualitative physical aspects and the quantitative description of time and frequency resolved absorption spectroscopy of high molecular Rydberg states are discussed. The frequency is that of the excitation laser and the time is the independently variable delay before detection. The discussion allows for the presence of a weak external electrical field. The essential new ingredient is the finite slice of Rydberg states that are detected (=are in the detection window) and the variation of this population with time due to the coupling of the Rydberg electron with the molecular core. Line shapes are provided showing the effect of the depth of the detection window and the advantages and limitations imposed by the finite width of the excitation laser. The sharpening of the spectrum as the delay time to detection is increased is also illustrated. The quantitative theory is expressed in terms of the expectation value of a detection operator; describing the range of states that can be ionized by the delayed field, taken over a wave function. This wave function is the state of the system at the time of detection. However, even just at the end of the excitation stage, due to the interseries coupling, this wave function is not identical to the state that is directly optically accessed. The time correlation function of this wave function, obtained as a Fourier transform. of the frequency resolved spectrum, is shown to provide further insight into the dynamics, the more so when the excitation laser has a narrow width in frequency. (C) 1997 American Institute of Physics.