Annu. Rev. Astron. Astrophys. 2001. 39: 137-174
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The rotation of galaxies was discovered in 1914, when Slipher (1914) detected inclined absorption lines in the nuclear spectra of M31 and the Sombrero galaxy, and Wolf (1914) detected inclined lines in the nuclear spectrum of M81. This evidence led Pease (1918) to use the Mt. Wilson 60-inch to "investigate the rotation of the great nebula in Andromeda" by obtaining a minor axis long slit spectrum of M31 with an exposure of 84 hours taken during clear hours in August, September, and October, 1916, and a major axis spectrum taken over 79 hours in August, September, and October, 1917. The absorption lines extended only 1.5 arcminutes in radius along the major axis, less than 2% of the optical radius, but were sufficient to show the steep nuclear velocity rise. Later studies of M31's rotation by Babcock (1939) and Mayall (1951) extended major axis rotation velocities to almost 2° from the nucleus, but exposure times were tens of hours, and spectrographs had stability problems. Interestingly, both Babcock's velocities for M31 and Humason's unpublished velocities for NGC 3115 showed the last measured point to have a rotation velocity of over 400 km s-1 (almost 2 times actual), but consequently raised questions of mass distribution.

At the dedication of the McDonald Observatory in 1939, Oort's (1940) comment that "...the distribution of mass [in NGC 3115] appears to bear almost no relation to that of the light" seems from the view in 2000 to have attracted little attention. His conclusion concerning the mass distribution in NGC 3115 is worth quoting, even 60 years later. "In the outer parts of the nebula the ratio f of mass density to light density is found to be very high; and this conclusion holds for whatever dynamical model we consider. The spectrum of the nebula shows the characteristics of G-type dwarfs. Since f cannot be much larger than 1 for such stars, they can account for roughly only 1/2 percent of the mass; the remainder must consist either of extremely faint dwarfs having an average ratio of mass to light of about 200 to 1 or else of interstellar gas and dust". From a reanalysis of the (scattered) velocities for M31, Schwarzschild (1954) concluded that the approximately flat rotation curve was "not discordant with the assumption of equal mass and light distribution."

The modern era of optical observations of rotation velocities within spiral galaxies dates from Page's (1952) and especially Margaret and Geoffrey Burbidge's (1960) observations which exploited the new red sensitivity of photographic plates to observe the Halpha and [NII] emission lines arising from HII regions within spiral disks. Within a decade, rotation curves existed for a few dozen galaxies, most of them extending only over the initial velocity rise and the turnover of the velocities.

Early radio observations of neutral hydrogen in external galaxies showed a slowly falling rotation curve for M31 (van de Hulst et al. 1957) and a flat rotation curve for M33 (Volders 1959). The first published velocity field ("spider diagram") was of M31 (Argyle 1965). For M33, the flatness could be attributed to the side lobes of the beam, and was consequently ignored. Louise Volders must also have realized that a flat rotation curve conflicted with the value of the Oort constants for our Galaxy, which implied a falling rotation curve at the position of the sun. Jan Oort was one of her thesis professors. By the 1970s, flat rotation curves were routinely detected (Rogstad and Shostak 1972), but worries about side bands still persisted, and a variation in M/L across the disk was a possible explanation (Roberts and Rots 1973).

Surveys of galaxy observations from these early years by de Vaucouleurs (1959) and of galactic dynamics by Lindblad (1959) reveal the development of the observations and the interpretation of the spiral kinematics. They are historically notable because they contains early references, many of which have faded into oblivion. More recent (but still early) reviews include de Vaucouleurs & Freeman (1973), Burbidge & Burbidge (1975), van der Kruit and Allen (1978).

Rotation curves are tools for several purposes: for studying the kinematics of galaxies; for inferring the evolutionary histories and the role that interactions have played; for relating departures from the expected rotation curve Keplerian form to the amount and distribution of dark matter; for observing evolution by comparing rotation curves in distant galaxies with galaxies nearby. Rotation curves derived from emission lines such as Halpha, HI and CO lines are particularly useful to derive the mass distribution in disk galaxies, because they manifest the motion of interstellar gases of population I, which have much smaller velocity dispersion, of the order of 5 - 10 km s-1, compared to the rotation velocities. This allows us to neglect the pressure term in the equation of motion for calculating the mass distribution in a sufficiently accurate approximation.

Here, we review the general characteristics of rotation curves for spiral galaxies as kinematic tracers, in relation to galaxy properties, such as Hubble types, activity, structure, and environment. These parameters are fundamental input for understanding the dynamics and mass distribution, evolution, and formation of spiral galaxies. Methods for analysis are described. In general, the discussion is restricted to studies since 1980. Higher-order, non-axisymmetric velocity components due to spiral arms and bars are not emphasized here. Although rotation curves of spiral galaxies are a major tool for determining the distribution of mass in spiral galaxies, we stress the observations rather than the mass determinations or the deconvolutions into luminous and dark matter.

Numerous discussions of rotation properties are included in the conference proceedings, Galaxy Dynamics (Merritt et al. 1999), Dynamics of Galaxies (Combes et al. 2000), Galaxy Disks and Disk Galaxies (Funes & Corsini 2001). Reviews of dark matter as deduced from galaxy rotation curves can be found in Trimble (1987), Ashman (1992), and Persic & Salucci (1997, and papers therein).

Spheroidal galaxies have been reviewed earlier (Faber & Gallagher 1979; Binney 1982; de Zeeuw & Franx 1991). Generally, measures of velocity and velocity dispersions are necessary for mass determinations in early type galaxies, although methods which we describe below are applicable to the cold disks often found in the cores of ellipticals, in extended disks of low-luminosity ellipticals (Rix et al. 1999), and in S0 galaxies.

Data for several million galaxies are available from huge databases accessible on the World Wide Web. Hypercat (Lyon/Meudon Extragalactic Database classifies references to spatially resolved kinematics (radio/optical/1-dimension/2-dim/velocity dispersion, and more) for 2724 of its over 1 million galaxies. NED (NASA/IPAC Extragalactic Database /index.html) contains velocities for 144,000 galaxies. The number of measured velocity points is tabulated for each galaxy reference. Both of these sites contain extensive literature references for galaxy data. High spatial (HST) STIS spectroscopy preprints are found in

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