  Relativistic fluid dynamics finds application in astrophysics, cosmology and
the physics of high-energy heavy-ion collisions. In this thesis, we present our
work on the formulation of relativistic dissipative fluid dynamics within the
framework of relativistic kinetic theory. We employ the second law of
thermodynamics as well as the relativistic Boltzmann equation to obtain the
dissipative evolution equations.
  We present a new derivation of the dissipative hydrodynamic equations using
the second law of thermodynamics wherein all the second-order transport
coefficients get determined uniquely within a single theoretical framework. An
alternate derivation of the dissipative equations which does not make use of
the two major approximations/assumptions namely, Grad's 14-moment approximation
and second moment of Boltzmann equation, inherent in the Israel-Stewart theory,
is also presented. Moreover, by solving the Boltzmann equation iteratively in a
Chapman-Enskog like expansion, we have derived the form of second-order viscous
corrections to the distribution function. Furthermore, a novel third-order
evolution equation for shear stress tensor is derived. Finally, we generalize
the collision term in the Boltzmann equation to include non-local effects. We
find that the second-order dissipative equations derived using this modified
Boltzmann equation contains all possible terms allowed by symmetry.
  In the case of one-dimensional scaling expansion, we demonstrate the
numerical significance of these formulations on the evolution of the hot and
dense matter created in ultra-relativistic heavy-ion collisions. We also study
the effect of these new formulations on particle (hadron and thermal dilepton)
spectra and femtoscopic radii.
