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In this paper, we establish a theory of Special Relativity valid for theentire speed range without the assumption of constant speed of light. Twoparticles species are defined, one species of particles have rest frames withrest mass, and another species of particles do not have rest frame and can notdefine rest mass. We prove that for the particles which have rest frames, theGalilean transformation is the only linear transformation of space-time thatallows infinite speed of particle motion. Hence without any assumption, anupper bound of speed is required for all non-Galilean linear transformations.We then present a novel derivation of the mass-velocity and the mass-energyrelations in the framework of relativistic dynamics, which is solely based onthe principle of relativity and basic definitions of relativistic momentum andenergy. The generalized Lorentz transformation is then determined. The newrelativistic formulas are not related directly to the speed of light $c$, butare replaced by a Relativity Constant $C_R$ which is an universal speedconstant of the Nature introduced in relativistic dynamics. Particles havingrest mass are called tardyons moving slower than $C_R$. Particles havingneither 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 tachyonat infinite speed. Moreover, the particles with constant-speed $C_R$, alsohaving neither rest frames nor rest mass, are called $constons$. For allparticles, $p^2=\vec{p}^2-({E^2}/{C_R^2})$ remains invariant undertransformation between inertia frames. The invariant reads $p^2=-m_0^2C_R^2 <0$for tardyons, $p^2 =0$ for constons and $p^2=|\vec{p}_\infty|^2 >0$ fortachyons, respectively.

Special Relativity for the Full Speed Range -- speed slower than $C_R$ also equal to and faster than $C_R$