  In this thesis, entanglement under fully relativistic settings are discussed.
The thesis starts with a brief review of the relativistic quantum mechanics. In
order to describe the effects of Lorentz transformations on the entangled
states, quantum mechanics and special relativity are merged by construction of
the unitary irreducible representations of Poincar{\'e} group on the infinite
dimensional Hilbert space of state vectors. In this framework, the issue of
finding the unitary irreducible representations of Poincar{\'e} group is
reduced to that of the little group. Wigner rotation for the massive particles
plays a crucial role due to its effect on the spin polarization directions.
Furthermore, the physical requirements for constructing the correct
relativistic spin operator is also studied. Then, the entanglement and Bell
type inequalities are reviewed. Special attention has been devoted to two
historical papers, by EPR in 1935 and by J.S. Bell in 1964. The main part of
the thesis is based on the Lorentz transformation of the Bell states and the
Bell inequalities on these transformed states. It is shown that entanglement is
a Lorentz invariant quantity. That is, no inertial observer can see the
entangled state as a separable one. However, it was shown that the Bell
inequality may be satisfied for the Wigner angle dependent transformed
entangled states. Since the Wigner rotation changes the spin polarization
direction with the increased velocity, initial dichotomous operators can
satisfy the Bell inequality for those states. By choosing the dichotomous
operators taking into consideration the Wigner angle, it is always possible to
show that Bell type inequalities can be violated for the transformed entangled
states.
