The basic equations for constructing a stellar atmosphere (hydrostatic equilibrium, flux constancy, radiative transfer, convective instability) are briefly summarized. While the parameters Teff (effective temperature) and g (surface gravity) are directly contained in these equations, the element abundances ∈i enter only indirectly through the thermodynamic properties (such as electron pressure, entropy, …) and the absorption and scattering coefficients of stellar matter.

The equation of state, convection, the effects of the absorption coefficients (particularly of line absorption) on the temperature stratification, and the role of velocity fields (microturbulence) are discussed in some detail, emphasizing their dependence on the abundances.

From a given model atmosphere, a ‘theoretical spectrum’ (colours, bolometric correction, line strengths etc.) can be calculated. The (relative) fluxes emerging at the surface are essentially determined by the temperature gradient and the absorption coefficients at the frequencies under consideration. The basic goal of quantitative classification, however, is the inverse problem, namely to deduce the stellar parameters from selected observed spectral criteria. Aspects relevant to this problem such as the question of uniqueness and the occurrence of possible systematic errors (even when using differential analysis techniques) are briefly sketched and illustrated by some examples.