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The distribution of matter in cosmological structures is a fundamental property of nature as the mass of a system is likely the major driver of its evolution. This is especially true for stars whose evolution depend almost fully on their initial mass (and chemical composition) on the main sequence, as embodied by the (idealistic) Vogt-Russell theorem. Mass also plays a fundamental role in galaxy evolution. Galaxies have largely been shaped through mergers and galaxy interactions in hierarchical fashion whereby small systems merged into bigger ones. At early times, star formation was most effective in massive galaxies but as the Universe aged, star formation was likely quenched in those massive systems but continued in smaller galaxies, a phenomenon now called "downsizing". Oldest stars are thus found in the most massive systems. The complex interplay between star formation efficiency and quenching is likely modulated by a galaxy's total mass.

Measurements of the distribution of matter in the Universe enable a variety of tests of structure formation models on different scales. For instance, the distribution of galaxy masses on all scales enables the closest possible, though not direct, comparison of predicted mass functions for baryonic and non-baryonic matter in the Universe. The relative fraction of baryonic to non-baryonic matter is also indicative of fundamental, yet poorly understood, processes in galaxy formation which typically give rise to tight scaling relations based on the stellar and dynamical masses of galaxies.

Because galaxy masses play such a critical role in our understanding of the formation and evolution of cosmic structures, we wish to review the variety and reliability of mass estimators for gas-poor and gas-rich galaxies and discuss our ability to derive from those estimators meaningful onstraints of theoretical galaxy formation models. While certain techniques enable only the measurement of galaxy masses on large scales, others allow the decomposition of individual mass components such as gas, stars and dark matter at different galactocentric radii. The latter methods probe the gravitational potential through the dynamics of visible tracers where baryons are (sub-)dominant. Although many galaxies may be safely assumed to be virialized, uncertainties in their mass estimates remain, for instance due to anisotropies in the velocity distributions. Furthermore, baryon-dominated regions remain poorly understood, which complicates a direct comparison of galaxy formation models to observational data.

Many techniques exist for the determination of galaxy masses. The most popular involves the measurement of Doppler shifts of nebular and/or stellar atomic lines due to internal dynamics. Stellar motions can also be resolved in the closest galaxies, such as our The Milky Way, Andromeda, and other Local Group stellar systems; galaxy masses of more distant systems otherwise rely on integrated spectra. Another mass estimator consists of converting the galaxy light profile into a mass profile using a suitable stellar mass-to-light ratio (usually derived from stellar population models). A more global approach has also involved the mapping of gravitational lensing effects, both strong and weak. This list is not meant to be complete, as we review below. However, in all cases, galaxy mass estimates account for matter encompassed within a specified radius and are thus always a lower limit to the total galaxy mass.

This review has evolved from discussions which took place during the celebrations of Vera Rubin's career at Queen's University in June 2009 1. All the authors of this review were indeed present at that conference. While each section of this review was initially written by separate teammates, the final product reflects the full team's imprimatur. This review was inspired by, and is meant as a modern revision of, early treatises on the masses and mass-to-light ratios of galaxies by Burbidge & Burbidge (1975) and Faber & Gallagher (1979), respectively.

The review is organized as follows: we first present in Section 2 the central topic of stellar M / L determinations from stellar population models. This is followed by a discussion of the mass estimates for gas-rich galaxies in Section 3, including the special (resolved) case of the Milky Way in Section 4. Gas-poor galaxies are addressed in Section 5 and weak and strong lensing techniques are presented in Section 6 and Section 7, respectively. Conclusions, with a view towards future developments, are presented at the end of each section.

This review is naturally incomplete; conspicuously missing topics include the measurement of stellar and dynamical masses of high redshift galaxies (e.g. Förster Schreiber et al. 2006; Bezanson et al. 2011; Alaghband-Zadeh et al. 2012), the direct comparison of stellar and dynamical mass estimates (e.g. de Jong & Bell 2007; Taylor et al. 2010), mass function determinations (e.g. stellar mass functions: Bundy et al. 2006; Pozzetti et al. 2010; Maraston et al. 2012) (e.g. dynamical mass functions: Trujillo-Gomez et al. 2011; Papastergis et al. 2011; Papastergis et al. 2012), constraints on halo masses by statistical techniques such as those involving satellite kinematics (More et al. 2011a; Wojtak & Mamon 2013), group catalogs (Yang et al. 2009), and abundance matching (Behroozi et al. 2013), to name a few.

Furthermore, this review is restricted to mass analyses based on Newtonian dynamics. Alternatives exist, the most popular being MOND (e.g. Milgrom 1983), but a proper treatment of them is beyond the scope of this review. Readers interested in alternative models, MOND or others, are referred to the review by Famaey & McGaugh (2012).

1 See for workshop presentations and photographs. Back.

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