ecial and general relativity are introduced at the beginning of this thesis. Then the future singularities of the universe are studied. For that propose first it has been shown that, Friedmann equations are derived from solving Einstein equations for the homogenous and isotropic universe which is described by FRW metric. Pressure, energy density, scale factor and Hubble parameter are important quantities for studying the universe. Possibilities of the future singularities are investigated by solving the Friedmann equations, assuming an accelerating expanding the universe. The result will be changed if we consider some new physical effects in this scenario. The effects of conformal anomalies and bulk viscosity have already been studied in several papers. It was shown that the bulk viscosity changes the time of singularity, but conformal anomaly can change the type ( II ) singularity to the type ( III ) singularity. Here we explore the effect of the Entropic force on the singularities. Because of the Entropic force, two correction terms are added to the Friedmann equations that are the results of surface term in the Einstein- Hilbert action. These terms are proportional to the Hubble parameter and it’s first derivative with respect to the time. They affect the singularity type ( II ), because they change the behavior of pressure or energy density. For some values of the parameters in this theory, pressure will be finite at the singularity time. So, both the pressure and energy density are finite at the singularity point and the singularity type ( II ) changes to the type ( IV ). For some other values the energy density will be infinite at the singularity time so, both pressure and energy density are infinite and the sudden future singularity (type (II)) changes to type ( III ) singularity. We also consider a running gravitational coupling and it’s effects on the future singularities of the universe. Because of asymptotic safety, it’s necessary for gravitational coupling to run with an energy scale. Here the gravitational coupling, “G” is studied as a function of energy density of the universe. Our results show that running gravitational coupling changes the type ( II ) singularity to a new kind of singularity, which is similar to type ( IV ). Also the time evolution of the universe will be changed in other cases. Then we consider the effect of both Entropic force and running gravitational coupling on the future singularities. It is shown that the behavior of the pressure and energy density does not change in the type ( I ) singularity. The singularity type ( II ) changes to a new kind of singularity which is similar to type ( III ). If we introduce the effective Hubble parameter, we find that singularity type ( II ) clearly changes to type ( III ), and type ( I ) that is a strong singularity in both Tipler and Krolak definition ,will changes to the singularity type ( III ), which is a strong singularity in Tipler definition but a weak singularity in Krolak definition. Keywords: Cosmology, Singularity, Entropic Force, Running Gravitational Coupling.