### 1. INTRODUCTION

Rotation of spiral galaxies is measured by spectroscopic observations of
emission lines such as Hα, HI and CO lines from disk objects,
namely population I objects and interstellar gases. In these lines the
velocity dispersion is negligibly small compared to rotational velocity,
which implies that the pressure term is negligible in the Virial
theorem, so that the dynamical balance between the gravitational and
centrifugal forces may be used to calculate the mass in sufficient
accuracy. Absorption lines are also used for bulge's kinematics
using velocity dispersion and rotation. The dynamical approach is
essential particularly for measurement of the mass of the dark matter
and black holes, which are not measurable in surface photometry assuming
a mass-to-luminosity ratio.

In sections 2 and 3
we review the various methods to derive rotation
curves of the Milky Way and spiral galaxies, respectively, and describe
the general characteristics of observed rotation curves. The progress in
the rotation curve studies will be also reviewed briefly.
In section 4 we review the methods to
determine the mass distributions in disk galaxies using the rotation
curves, and describe their dynamical mass structures.

By definition, a rotation curve is the mean circular velocity around the
nucleus as a single function of radius. Non-circular streaming motions
such as due to spiral arms, bars, and/or expansion/contraction motions
are not considered here. Limitation of the current rotation curve
analyses is discussed in section 2.
Elliptical galaxies, for which rotation curve analysis is not
applicable, are beyond the scope of this review. Considerations that
employ unconventional physical laws such as MOND (modified Newtonian
dynamics) are also out of the scope of this review.

There are a number of articles and reviews on rotation curves and mass
determination of galaxies, that include
Sofue and Rubin (2001)
and
Sofue (2013a),
and the literature therein. Individual references will be given in the
related sections in this review.