Experimental and theoretical investigations on linear and non-linear r
esonance Raman scattering from simple systems are discussed. We first
report on studies of continuum resonance Raman scattering in halogen a
nd interhalogen molecules, where we show how the experiments can be si
mulated applying time-independent as well as time-dependent theory. Pr
ecise determinations of repulsive excited state functions, scattering
delay times, a reflection and a symmetry principle are discussed as we
ll. Next we report on absorption, resonance Raman and resonance cohere
nt anti-Stokes Raman scattering (CARS) spectroscopy in partially polym
erized diacetylene single crystals. A theoretical model is presented w
hich allows calculation of one-, two- and four-photon spectra as well
as resonance Raman and resonance CARS excitation profiles. Comparisons
are made to experimental results. Finally we describe recent experime
ntal results on absorption, resonance Raman and resonance CARS spectro
scopy of the permanganate ion doped in potassium perchlorate single cr
ystals.