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The first galaxies have captivated theorists and observers alike for more than four decades. They were recognized as key drivers of early cosmic evolution at the end of the cosmic dark ages, when the Universe was just a few 100 million years old (e.g., Rees 1993; Barkana & Loeb 2001). Within the standard Lambda cold dark matter (LambdaCDM) cosmology, where structure forms hierarchically through mergers of smaller dark matter (DM) halos into increasingly larger ones, the first galaxies were the basic building blocks for galaxy formation (e.g., Blumenthal et al. 1984; Springel et al. 2005). The highly complex physics associated with galaxy assembly and evolution still largely defies our understanding, but the first galaxies may provide us with an ideal, simplified laboratory for study (e.g., Loeb 2010).

A crucial ingredient to any theory of how the first galaxies assembled, and how they impacted subsequent cosmic history, is the feedback exerted by the stars formed inside them or their smaller progenitor systems (e.g., Wise & Abel 2008; Greif et al. 2010). Understanding the first galaxies is therefore intricately linked to the formation of the first, so-called Population III (Pop III) stars (Bromm et al. 2009). The stellar feedback is usually divided into radiative and supernova (SN) feedback (Ciardi & Ferrara 2005). The radiative effect consists of the build-up of H II regions around individual massive Pop III stars, thus initiating the extended process of cosmic reionization (Sokasian et al. 2004; Barkana & Loeb 2007). The SN feedback has a direct mechanical aspect, where the blastwave triggered by the explosion imparts heat and momentum to the surrounding intergalactic medium (IGM). Supernovae also disperse heavy elements into the IGM, thereby affecting the subsequent mode of star formation in the polluted gas. An early episode of enriching the primordial, pure H/He Universe with metals is therefore another long-term legacy left behind by the first stars and galaxies, together with reionization.

There is a further, observational, reason for the current flurry of activity in understanding the first galaxies. Researchers wish to predict the properties of the sources to be probed with upcoming or planned next-generation facilities, such as the James Webb Space Telescope (JWST), the Atacama Large Millimeter Array (ALMA), or extremely large telescopes to be constructed on the ground. The main efforts in the latter category are the Giant Magellan Telescope, the Thirty Meter Telescope, and the European Extremely Large Telescope, which are pursued concurrently at the present time. In each case, we need to work out the overall luminosities, spectral energy distributions or colors, and the expected number densities of sources as a function of redshift. Complementary to the direct detection approach are possible signatures of the first galaxies in the redshifted 21-cm background radiation (Furlanetto et al. 2006; Morales & Wyithe 2010). Here, a number of already operational or planned meter-wavelength radio telescopes, among them the Low Frequency Array (LOFAR), will soon commence the search for the 21-cm signatures. The effort of arriving at robust predictions for these facilities greatly benefits from recent advances in supercomputer technology, where large- (tera and peta-) scale, massively parallel systems provide us with unprecedented computational power to carry out ever more realistic simulations in the cosmological context.

Most large galaxies today harbor supermassive black holes (SMBHs) in their centers (e.g., Kormendy & Richstone 1995; Ferrarese & Ford 2005). An important question then is when and how galaxies first acquired such central black holes. Related is the problem of understanding the presence of ~ 109 Modot SMBHs that are inferred to power the luminous quasars discovered by the Sloan Digital Sky Survey (SDSS) at redshifts z gtapprox 6 (Fan, Carilli & Keating 2006). A popular theoretical model assumes that such very massive black holes grew from smaller seeds, present already in the smaller progenitor systems that merged into the massive SDSS quasar hosts (Li et al. 2007). The efficieny of growing a black hole via accretion of surrounding gas over the available time of several hundred million years, however, may have been quite limited. A possible way out is to begin the SMBH assembly process already with more massive seeds. The first galaxies have indeed been suggested as viable formation sites for such ~ 106 Modot seed black holes (see Section 5). Regardless of their exact properties and origin, such massive black holes would likely have influenced the structure and evolution of the first galaxies (e.g., Cattaneo et al. 2009).

The nature of the stellar populations in the first galaxies is crucial for the observational quest. According to some theories, the majority of the first galaxies already contained low-mass, Population II (Pop II), stars, and perhaps stellar clusters in general. This expectation is based on the theory of a `critical metallicity', Zcrit ~ 10-6 - 10-4 Zodot, above which the mode of star formation is thought to change from top-heavy to normal, bottom-heavy (e.g., Bromm et al. 2001; Schneider et al. 2002). Due to the pre-enrichment from Pop III stars in the galaxy's progenitor systems, the so-called minihalos (Haiman, Thoul & Loeb 1996; Tegmark et al. 1997; Yoshida et al. 2003), the first galaxies were likely already supercritical, thus experiencing Pop II star formation. The minihalos, consisting of DM halos with total mass ~ 106 Modot and collapsing at z ~ 20-30, are the formation sites for the first (Pop III) stars. Cooling inside of them relies on a trace amount ( ~ 10-3 by number) of molecular hydrogen. These halos have shallow potential wells, so that they are highly susceptible to negative feedback effects from Pop III stars. A subset of the first Pop II star, those with subsolar masses, will survive to the present, and can thus be probed as fossils of the dark ages in our immediate cosmic neighborhood. This approach, often termed stellar archaeology (e.g., Beers & Christlieb 2005; Frebel 2010), provides constraints on the SN yields of the first stars, as well as on the environment for star formation inside the first galaxies. A similar strategy has recently become feasible, where the stellar content and structural properties of low-mass dwarf galaxies in the Local Group are interpreted under the assumption that they are descendants of the first galaxies (e.g., Tolstoy, Hill & Tosi 2009; Ricotti 2010). Finally, these early galaxies are also discussed as formation sites for the oldest globular clusters (Bromm & Clarke 2002; Kravtsov & Gnedin 2005; Moore et al. 2006; Brodie & Strader 2006; Boley et al. 2009; Cooper et al. 2010).

The plan for this review is as follows. We begin by considering the seemingly straightforward question: What is the definition of a first galaxy? It turns out that there is no universally accepted definition, as is the case for what we mean by the formation of the first stars. Theorists and observers employ different concepts, and often do not agree even among themselves. We will try to clarify the situation (Section 2). We then turn to a survey of what is known from existing observations that push the envelope and begin to reach very high redshifts (Section 3). This is followed by a more extended discussion of the lessons gleaned from recent simulations, many of them studying the assembly of the first galaxies with considerable physical sophistication and within a realistic cosmological context (Section 4). Due to its importance, we devote a separate section to the early co-evolution of massive black holes and stellar systems, although our knowledge here also relies mostly on theory and numerical simulations (Section 5). The following two sections discuss the observational signature of the first galaxies, with a special focus on the JWST, but also addressing the stellar archaeology approach, as well as more indirect clues from the cumulative impact of the first galaxies on reionization, 21cm radiation, and the cosmic infrared background (Sections 6 - 7). We conclude with a brief outlook into the exciting decade ahead.

At the end of this introduction, we would like to point the reader to a few other reviews that cover material related to this subject here. For a general overview of the end of the cosmic dark ages, see the extensive review by Barkana & Loeb (2001), the more succinct one by Bromm et al. (2009), and the monographs by Stiavelli (2009) and Loeb (2010). Feedback processes are discussed in detail by Ciardi & Ferrara (2005), whereas the physics and observational picture of reionization are treated by Fan et al. (2006), Barkana & Loeb (2007), and Meiksin (2009). The formation of the first stars was reviewed by Bromm & Larson (2004) and Glover (2005). It is instructive to consider the huge lore of knowledge that we have on present-day star formation, when extrapolating to the primordial case. Comprehensive resources are the reviews by McKee & Ostriker (2007) and Zinnecker & Yorke (2007). The field of stellar archaeology has been summarized by Freeman & Bland-Hawthorn (2002), Beers & Christlieb (2005), Tolstoy, Hill & Tosi (2009), Frebel (2010), and Ricotti (2010). Finally, Mo, van den Bosch & White (2010) have written an excellent textbook that summarizes all aspects of galaxy formation and evolution in the proper cosmological context (also see Benson 2010).

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