Addressing the question of the formation and the evolution of galaxies in a cosmological context implies that we must understand their emission over the broadest electromagnetic spectrum. Using multi-wavelength data consistently enables to measure reliable physical parameters like star-formation rates and stellar masses.However, the drawback of this approach is that we do need more information in terms of data. We also need to handle them by using powerful computers and smart codes that are able to run ina reasonable amount of time and deal with a wealth of data and a huge number of models. A statistical approach is also mandatory to estimate the reliability of the results. In this chapter I will describe the different components and physical processesthat leave their imprints in the distribution of energy of galaxiesandhow physicalparameters related to their star formation history can be extracted from the fit of their spectral energy distribution. I willpresent physically-motivated codes which assume an energy balance between dust stellar absorption and re-emission

Stars play such a fundamental role in the evolution of galaxies, some of the key-questions in the field of galaxy evolution and cosmology are related to the history of their formation in galaxies. How do star formation and its history depend on the environment or on the mass of galaxies? When do stars form globally in the history of the universe ? When and how does starlight contribute to the re-ionization phase in the early universe?The goal of this book is to provide the reader an overall presentation of the theoretical and observational backgrounds about the definition and measurement of Star-Formation Rates in galaxies

The measured star-formation rates (SFRs) of galaxies comprise an important constraint on galaxy evolution and also on their cosmological boundary conditions. Any available tracer of the SFR depends on the shape of the mass-distribution of formed stars, i.e. on the stellar initial mass function(IMF). The luminous massive stars dominate the observed photon flux while the dim low-mass stars dominate the mass in the freshly formed population. Errors in the number ratio of the massive to low-mass stars lead to errors in SFR measurements and thus to errors concerning the gas-accretion ratesand the gas-consumption time-scales of galaxies. The stellar IMF has traditionally been interpreted to be a scale-invariant probability density distribution function (PDF), but it may instead be an optimal distribution function. In the PDF interpretation, the stellar IMF observed on the stales of individual star clusters is equal to the galaxy-wide IMF (gwIMF) which, by implication, would be invariant. In this chapter we discuss the fundamental properties of the IMF and of the gwIMF, the nature of both and their systematic variability as indicated by measurements and theoretical expectations, and we discuss the implications for the SFRs of galaxies.

In many ways the study of resolved stellar populations is the bestmethod for exploring properties of stellar populations. However, the method requires measurements to be obtained for individual stars, and this rapidly becomes challenging as the distance to extragalactic systems increases. The depths of resolved stellar samples in galaxies are primarily limited by the levels of stellarfluxes and effects of crowding. Currently most resolved stellar population studies are constrained to galaxies within a distance of about 20 Mpc. Fortunately, the short-lived massive stars, whose numbers trace SFRs, are luminous and thus among the most readily observed, especially when they are not obscured by interstellar dust. The number of stars above a fiducial luminosity in a set of spectroscopic band-passesare counted and corrected for incomplete sampling. The distribution of these stars is then compared to expectations of stellar population models to derive estimates for the observed mass in the form of stars detected in the data. Further modeling provides an interpretation in terms of stellar masses within age bins. In this chapter we provide a brief overview of the history and some of the techniques used to derive star-formation rates (SFRs) and the associated star-formation histories of galaxies through observations