: General relativity of theory has been known as a main theory in description of many cosmic observations. Observational data indicates that the universe is expanding with positive accelerate. Dark energy is used as a main candidate for explanation of this accelerated expansion. Existence of dark energy can lead to singularities in Friedmann equations. These singularities depending on the behavior of pressure, energy density and scale factor that is the scale of universe magnitude are divided in different types. Recently has been introduced a new scenario was called Little Rip that is a universe in which the dark energy density increase without bound but the universe never reaches a finite-time singularity. Features of Little Rip is similar to the universe that ends up with type ( ) singularity but in this case time of occurrence singularity is infinite. There are many causes that can lead to change the behavior of singularities in occurrence time. One of them is the varying speed of light. According to varying speed of light theory light is traveling faster in the early periods of the existence of the universe. In this thesis we will show that the varying speed of light as a function the universe’s life time can change the behavior of singularities type ( ) and type ( ). also we will investigate the varying speed of light effect in Little Rip. Modified theories of gravity have been proposed as the other candidate to explain accelerated expansion of the universe. In the recent years F(R) theory has been studied as the simplest modified theory of gravity. In this theory the gravitational action described by an arbitrary function of scalar curvature R. friedmann equations singularities also exist in field equations in this theory. F(R) models corresponding to any type of singularities are countable. Also the possibility of Little Rip occurrence exist in this theory. In this thesis we will obtain the specific model for Little Rip cosmology in F(R) modified theory. There is the fundamental relation between gravity and thermodynamics. Therefore one of ways that we can sure about correctness of one model is investigation the laws of thermodynamics in that model. In this thesis we will investigate the second law of thermodynamics in near the future finite-time singularities and in model that we have obtained for Little Rip cosmology. Key Words: Einstein field equations, Friedmann equations, Singularity, Little Rip, Varying speed of light, Einstein-Hilbert action, Modified gravity, Laws of thermodynamics