In section 1 practical details concerning the equivalence of observational and theoretical descriptions of stellar spectra are reviewed, particularly the difficulty of identifying the observed reference level (continuum) with the theoretical continuum in the case when many lines are present. In this connection thought must be given to how integrals over frequency should be normalised and evaluated because the effective continuous absorption coefficient does not remain constant over the range from 0 to ∞. The choice of spectroscopic details by which to determine Teff, log g and abundances requires careful consideration.

In section 2 the factors by which an extended atmosphere are recognized are summarized and the question is posed do all stars have extended atmospheres. Another question requiring an answer is whether the concepts microturbulence and macroturbulence are physically real concepts or whether they are merely fitting parameters to make a simple LTE theory account for the observed spectra of supergiants in which rather wide lines occur and many multiplets show rather steep gradients. In section 3 the types of line sensitive to non-LTE conditions are described. These are resonance lines, lines arising from metastable levels, subordinate lines for which the upper level is sufficiently separated from the continuum and other levels that this upper level is chiefly populated by radiative processes from the ground or other low lying levels and lines which go into emission in low density atmospheres as a result of optical-pumping (fluorescent) processes. Such lines should not be used for abundance determinations by means of LTE theory though this is frequently done.

Theoretical considerations are discussed in Section 4 where first the problem of the two-level atom is sketched and then the problem is generalised to a many-level atom. The parameter λ which gives the probability that a photon is lost from the line by de-excitation processes other than spontaneous emission is defined and it is pointed out that non-LTE physics has the effect of adding a scattering term to the expression for the source function. One example is given of the effect of changing the line source function from the Planck function to a form suitable for isotropic coherent scattering. The line becomes deeper and wider for the same number of atoms. Interpretational problems in stellar spectra are discussed in section 5. It is noted that many lines in main-sequence early type spectra show the effects of departures from LTE. These effects are shown to a conspicuous degree by the spectra of shell stars. The example of He I 5876 in 10 Lacertae, 09V, is discussed and the implication for interpreting the He I lines in all B type main-sequence stars are touched upon. Helium-weak and helium-strong spectra probably indicate variations in density of the outer U atmosphere rather than true abundance differences. The spectra of supergiants are also considered and it is pointed out that the Ia supergiants of type B may be hydrogen-poor.

Finally in section 6 the problem of choosing simplified physical representations of line forming when non-LTE physics must be used is discussed. Some relevant points concerning the observed spectral lines used for spectral classification are illustrated by means of partial energy-level diagrams.