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Evolutionary synthesis models as a tool and guide towards the first galaxies

We summarize the principles and fundamental ingredients of evolutionary synthesis models, which are stellar evolution, stellar atmospheres, the IMF, star-formation histories, nebular emission, and also attenuation from the ISM and IGM. The chapter focusses in particular on issues of importance for predictions of metal-poor and Population III dominated galaxies. We review recent predictions for the main physical properties and related observables of star-forming galaxies based on up-to-date inputs. The predicted metallicity dependence of these quantities and their physical causes are discussed. The predicted observables include in particular the restframe UV-to-optical domain with continuum emission from stars and the ionized ISM, as well as emission lines from H, He, and metals. Based on these predictions we summarize the main observational signatures (emission line strengths, colors etc.), which can be used to distinguish "normal" stellar populations from very metal-poor objects or even Pop III. Evolutionary synthesis models provide an important and fundamental tool for studies of galaxy formation and evolution, from the nearby Universe back to first galaxies. They are used in many applications to interpret existing observations, to predict and guide future missions/instruments, and to allow direct comparisons between state-of-the-art galaxy simulations and observations.