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The origin and evolution of galaxies are among the most intriguing and complex chapters in the formation of cosmic structure, and observations in this field have accumulated at an astonishing pace. Multiwavelength imaging surveys with the Hubble (HST) and Spitzer space telescopes and ground-based facilities, together with spectroscopic follow-up with 8-m-class telescopes, have led to the discovery of galaxies with confirmed redshifts as large as z = 7.5 (Finkelstein et al. 2013), as well as compelling photometric candidates as far back as z ≈ 11 (Coe et al. 2013) when the Universe was only 3% of its current age. Following the seminal work of Steidel et al. (1995), color-selection criteria that are sensitive to the presence of intergalactic H I absorption features in the spectral energy distribution (SED) of distant sources have been used to build increasingly large samples of star-forming galaxies at 2.5 ltapprox z ltapprox 9 (e.g., Madau et al. 1996, Steidel et al. 2003, Giavalisco et al. 2004a, Bouwens et al. 2011b). Infrared (IR)-optical color selection criteria efficiently isolate both actively star-forming and passively evolving galaxies at z ≈ 2 (Franx et al. 2003, Daddi et al. 2004). Photometric redshifts have become an unavoidable tool for placing faint galaxies onto a cosmic timeline. Spitzer, Herschel, and submillimeter telescopes have revealed that dusty galaxies with star-formation rates (SFRs) of order 100 M year-1 or more were abundant when the Universe was only 2-3 Gyr old (Barger et al. 1998, Daddi et al. 2005, Gruppioni et al. 2013). Deep near-infrared (NIR) observations are now commonly used to select galaxies on the basis of their optical rest-frame light and to chart the evolution of the global stellar mass density (SMD) at 0 < z < 3 (Dickinson et al. 2003). The Galaxy Evolution Explorer (GALEX) satellite has quantified the ultraviolet galaxy luminosity function (LF) of galaxies in the local Universe and its evolution at z ltapprox 1. Ground-based observations and, subsequently, UV and IR data from GALEX and Spitzer have confirmed that star-formation activity was significantly higher in the past (Lilly et al. 1996, Schiminovich et al. 2005, Le Floc'h et al. 2005). In the local Universe, various galaxy properties (colors, surface mass densities, and concentrations) have been observed by the Sloan Digital Sky Survey (SDSS) to be "bimodal" around a transitional stellar mass of 3 × 1010 M (Kauffmann et al. 2003), showing a clear division between faint, blue, active galaxies and bright, red, passive systems. The number and total stellar mass of blue galaxies appear to have remained nearly constant since z ~ 1, whereas those of red galaxies (around L) have been rising (Faber et al. 2007). At redshifts 0 < z < 2 at least, and perhaps earlier, most star-forming galaxies are observed to obey a relatively tight "main-sequence" correlation between their SFRs and stellar masses (Brinchmann et al. 2004, Noeske et al. 2007, Elbaz et al. 2007, Daddi et al. 2007). A minority of starburst galaxies have elevated SFRs above this main sequence as well as a growing population of quiescent galaxies that fall below it.

With the avalanche of new data, galaxy taxonomy has been enriched by the addition of new acronyms such as LBGs, LAEs, EROs, BzKs, DRGs, DOGs, LIRGs, ULIRGs, and SMGs. Making sense of it all and fitting it together into a coherent picture remains one of astronomy's great challenges, in part because of the observational difficulty of tracking continuously transforming galaxy sub-populations across cosmic time and in part because theory provides only a partial interpretative framework. The key idea of standard cosmological scenarios is that primordial density fluctuations grow by gravitational instability driven by cold, collisionless dark matter, leading to a "bottom-up" ΛCDM (cold dark matter) scenario of structure formation (Peebles 1982). Galaxies form hierarchically: Low-mass objects ("halos") collapse earlier and merge to form increasingly larger systems over time - from ultra-faint dwarfs to clusters of galaxies (Blumenthal et al. 1984). Ordinary matter in the Universe follows the dynamics dictated by the dark matter until radiative, hydrodynamic, and star-formation processes take over (White & Rees 1978). The "dark side" of galaxy formation can be modeled with high accuracy and has been explored in detail through N-body numerical simulations of increasing resolution and size (e.g., Davis et al. 1985, Dubinski & Carlberg 1991, Moore et al. 1999, Springel et al. 2005, 2008, Diemand et al. 2008, Stadel et al. 2009, Klypin et al. 2011). However, the same does not hold for the baryons. Several complex processes are still poorly understood, for example, baryonic dissipation inside evolving CDM halos, the transformation of cold gas into stars, the formation of disks and spheroids, the chemical enrichment of gaseous material on galactic and intergalactic scales, and the role played by "feedback" [the effect of the energy input from stars, supernovae (SNe), and massive black holes on their environment] in regulating star formation and generating galactic outflows. The purely phenomenological treatment of complex physical processes that is at the core of semi-analytic schemes of galaxy formation (e.g., White & Frenk 1991, Kauffmann et al. 1993, Somerville & Primack 1999, Cole et al. 2000) and - at a much higher level of realism - the "subgrid modeling" of star formation and stellar feedback that must be implemented even in the more accurate cosmological hydrodynamic simulations (e.g., Katz et al. 1996, Yepes et al. 1997, Navarro & Steinmetz 2000, Springel & Hernquist 2003, Keres al. 2005, Ocvirk et al. 2008, Governato et al. 2010, Guedes et al. 2011, Hopkins et al. 2012, Kuhlen et al. 2012, Zemp et al. 2012, Agertz et al. 2013) are sensitive to poorly determined parameters and suffer from various degeneracies, a weakness that has traditionally prevented robust predictions to be made in advance of specific observations.

Ideally, an in-depth understanding of galaxy evolution would encompass the full sequence of events that led from the formation of the first stars after the end of the cosmic dark ages to the present-day diversity of forms, sizes, masses, colors, luminosities, metallicities, and clustering properties of galaxies. This is a daunting task, and it is perhaps not surprising that an alternative way to look at and interpret the bewildering variety of galaxy data has become very popular in the past two decades. The method focuses on the emission properties of the galaxy population as a whole, traces the evolution with cosmic time of the galaxy luminosity density from the far-UV (FUV) to the far-infrared (FIR), and offers the prospect of an empirical determination of the global history of star formation and heavy element production of the Universe, independently of the complex evolutionary phases of individual galaxy subpopulations. The modern version of this technique relies on some basic properties of stellar populations and dusty starburst galaxies:

  1. The UV-continuum emission in all but the oldest galaxies is dominated by short-lived massive stars. Therefore, for a given stellar initial mass function (IMF) and dust content, it is a direct measure of the instantaneous star-formation rate density (SFRD).

  2. The rest-frame NIR light is dominated by near-solar-mass evolved stars that make up the bulk of a galaxy's stellar mass and can then be used as a tracer of the total SMD.

  3. Interstellar dust preferentially absorbs UV light and re-radiates it in the thermal IR, so that the FIR emission of dusty starburst galaxies can be a sensitive tracer of young stellar populations and the SFRD.

By modeling the emission history of all stars in the Universe at UV, optical, and IR wavelengths from the present epoch to z ≈ 8 and beyond, one can then shed light on some key questions in galaxy formation and evolution studies: Is there a characteristic cosmic epoch of the formation of stars and heavy elements in galaxies? What fraction of the luminous baryons observed today were already locked into galaxies at early times? Are the data consistent with a universal IMF? Do galaxies reionize the Universe at a redshift greater than 6? Can we account for all the metals produced by the global star-formation activity from the Big Bang to the present? How does the cosmic history of star formation compare with the history of mass accretion onto massive black holes as traced by luminous quasars?

This review focuses on the range of observations, methods, and theoretical tools that are allowing astronomers to map the rate of transformation of gas into stars in the Universe, from the cosmic dark ages to the present epoch. Given the limited space available, it is impossible to provide a thorough survey of such a huge community effort without leaving out significant contributions or whole subfields. We have therefore tried to refer only briefly to earlier findings, and present recent observations in more detail, limiting the number of studies cited and highlighting key research areas. In doing so, we hope to provide a manageable overview of how the field has developed and matured in line with new technological advances and theoretical insights, and of the questions with which astronomers still struggle nowadays.

The remainder of this review is organized as follows. The equations of cosmic chemical evolution that govern the consumption of gas into stars and the formation and dispersal of heavy elements in the Universe as a whole are given in Section 2. We turn to the topic of measuring mass from light, and draw attention to areas of uncertainty in Section 3. Large surveys, key data sets and the analyses thereof are highlighted in Section 4. An up-to-date determination of the star-formation history (SFH) of the Universe is provided and its main implications are discussed in Serction 5. Finally, we summarize our conclusions in Section 6. Unless otherwise stated, all results presented here will assume a "cosmic concordance cosmology" with parameters (ΩM, ΩΛ, Ωb, h) = (0.3, 0.7, 0.045, 0.7).

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