  In this paper, we establish a theory of Special Relativity valid for the
entire speed range without the assumption of constant speed of light. Two
particles species are defined, one species of particles have rest frames with
rest mass, and another species of particles do not have rest frame and can not
define rest mass. We prove that for the particles which have rest frames, the
Galilean transformation is the only linear transformation of space-time that
allows infinite speed of particle motion. Hence without any assumption, an
upper bound of speed is required for all non-Galilean linear transformations.
We then present a novel derivation of the mass-velocity and the mass-energy
relations in the framework of relativistic dynamics, which is solely based on
the principle of relativity and basic definitions of relativistic momentum and
energy. The generalized Lorentz transformation is then determined. The new
relativistic formulas are not related directly to the speed of light $c$, but
are replaced by a Relativity Constant $C_R$ which is an universal speed
constant of the Nature introduced in relativistic dynamics. Particles having
rest mass are called tardyons moving slower than $C_R$. Particles having
neither rest frames nor rest mass are called $tachyons$ moving faster than
$C_R$, and with the real mass-velocity relation $m=|\vec{p}_\infty
|(v^2-C_R^2)^{-1/2}$ where $\vec{p}_\infty $ is the finite momentum of tachyon
at infinite speed. Moreover, the particles with constant-speed $C_R$, also
having neither rest frames nor rest mass, are called $constons$. For all
particles, $p^2=\vec{p}^2-({E^2}/{C_R^2})$ remains invariant under
transformation between inertia frames. The invariant reads $p^2=-m_0^2C_R^2 <0$
for tardyons, $p^2 =0$ for constons and $p^2=|\vec{p}_\infty|^2 >0$ for
tachyons, respectively.
