Blue supergiants of spectral types B and A are the visually brightest stars in spiral and irregular galaxies, with their most luminous members (at ) outshining entire dwarf galM 10 V axies. This characteristic allows us to use them as probes to study the local universe in great detail. In principle, already existing large telescopes and instrumentation facilitate quantitative spectroscopy of these objects as far as the Virgo and Fornax clusters of galaxies. Beyond their challenging stellar atmospheres and opportunities for testing sophisticated nonLTE physics, they offer numerous applications to modern astrophysics. Quantitative spectroscopy of supergiants will contribute to improving our understanding of massive-star evolution. Galactic abundance gradients and abundance patterns, as will be obtained from studies of large ensembles of supergiants in our own and other galaxies, will foster the understanding of galactochemical evolution. Finally, they are promising independent indicators for calibrating the extragalactic distance scale, by application of the wind momentum–luminosity and the flux-weighted gravity–luminosity relationships (R. P. Kudritzki et al. 1999, AA R. P. Kudritzki, F. Bresolin, & N. Przybilla 2003, ApJ, 582, L83). In view of this large potential, the objective of this thesis is to improve the status of quantitative spectroscopy of BA-type supergiants and to provide first applications on a sample of Galactic and extragalactic targets. It is shown that among the model atmospheres available at present, the best suited for analyses of supergiants are line-blanketed classical LTE models. An investigation of the impact of various parameters such as helium abundance and line blanketing on the atmospheric structure shows that for the most luminous objects, an accurate treatment of these parameters is essential for a quantitative analysis, whereas the less luminous supergiants react less sensitively. Spectrum synthesis is used to model the line spectra. It is the only technique capable of providing analyses of spectra of different qualities from low to high resolution and able to cope with heavy line blending at a broad range of signal-tonoise ratios. The stellar parameters are determined from purely spectroscopic indicators, from temperatureand gravity-sensitive ionization equilibria and the Balmer line wings. Elemental abundances are derived by modeling individual spectral features. Several tens of thousands spectral lines from 28 chemical species are included in the line formation, allowing almost the entire observed spectra to be reproduced. Non-LTE effects become important in blue supergiants, where a strong radiation field at low particle densities favors deviations from LTE. Comprehensive model atoms are therefore constructed for C i/ii, N i/ii, O i, and Mg i/ii in order to determine non-LTE level populations (N. Przybilla, K. Butler, & R. P. Kudritzki 2001, AA N. Przybilla & K. Butler 2001, AA N. Przybilla et al. 2000, AA N. Przybilla et al. 2001, A&A, 369, 1009). Highly accurate radiative and collisional atomic data recently determined for astrophysical and fusion research using the R-matrix method in the closecoupling approximation are incorporated. In addition, model atoms for H, He i, O ii, S ii/iii, Ti ii, and Fe ii are adopted from the literature, the atomic data being updated to more modern values in some cases. Thus, an improved treatment for the main elements of astrophysical interest is achieved. Extensive testing of the atomic data is performed for the nearby bright main-sequence standard Vega (A0 V), at welldetermined stellar parameters and atmospheric structure. A high-resolution and low-noise spectrum with large wavelength coverage from the visual to the near-IR is used for this purpose. Further tests are performed for the Galactic supergiants h Leo, HD 111613, HD 92207, and b Ori, with similar high-quality spectra in order to study the non-LTE effects across the parameter space. Accurate and consistent stellar parameters are derived for these. Non-LTE ionization equilibria of several elements—typically N i/ii, O i/ii, Mg i/ii, and S ii/iii—agree simultaneously, provided that a realistic treatment of line blocking is used. These parameters also constitute important input data for further studies of the stellar winds of these objects. Accounting for non-LTE reduces the random errors and removes systematic trends in the analyses. In particular, the improved treatment of electron collisions largely removes longstanding discrepancies in analyses of lines from different spin systems of a given ion. The computed non-LTE line profiles fit the observations well for the different species at a given elemental abundance. In the parameter range covered, all lines from He i, C i/ii, N i/ii, O i/ii, and S ii/iii are significantly