  This is a concise introduction to the topic of nonextensive Tsallis
statistics meant especially for those interested in its relation to high energy
proton-proton, proton-nucleus, and nucleus-nucleus collisions. The three types
of Tsallis statistics are reviewed. Only one of them is consistent with the
fundamental hypothesis of equilibrium statistical mechanics. The single
particle distributions associated with it, namely Boltzmann, Fermi-Dirac, and
Bose-Einstein, are derived. These are not equilibrium solutions to the
conventional Boltzmann transport equation which must be modified in a rather
nonintuitive manner for them to be so. Nevertheless the Boltzmann limit of the
Tsallis distribution is extremely efficient in representing a wide variety of
single particle distributions in high energy proton-proton, proton-nucleus, and
nucleus-nucleus collisions with only three parameters, one of them being the
so-called nonextensitivity parameter $q$. This distribution interpolates
between an exponential at low transverse energy, reflecting thermal
equilibrium, to a power law at high transverse energy, reflecting the
asymptotic freedom of QCD. It should not be viewed as a fundamental new
parameter representing nonextensive behavior in these collisions.
