  This paper is concerned with the relativistic Boltzmann equation without
angular cutoff. We establish the global-in-time existence, uniqueness and
asymptotic stability for solutions nearby the relativistic Maxwellian to the
special relativistic Boltzmann equation without any angular cutoff. We work in
the case of a spatially periodic box. We assume the generic hard-interaction
and soft-interaction conditions on the collision kernel that were derived by
Dudy\'nski and Ekiel-Je$\dot{\text{z}}$ewska (Comm. Math. Phys. 115(4):607-629,
1985), and our assumptions include the case of Israel particles (J. Math. Phys.
4:1163-1181, 1963). In this physical situation, the angular function in the
collision kernel is not locally integrable, and the collision operator behaves
like a fractional diffusion operator. We further derive the relativistic
analogue of the Carleman dual representation of Boltzmann collision operator.
This is the first global existence and stability result for relativistic
Boltzmann equation without angular cutoff and this resolves the open question
of perturbative global existence without the Grad's angular cut-off assumption.
