Although the observational evidences in favor of the recent accelerated expansion of the universe are mounting everyday , the driver of this acceleration which is suggested as dark energy has not been completely detected. In this thesiwe consider a holographic dark energy model in standard Einstein's gravity. The model is quite general as it allows the dark energy to interact with the the dark matter. We find that for where ??= , the system starts with a decelerated expansioand settle down to an accelerated expansiofor the universe with dark matter completely giving way to dark energy. We will see that the interaction rate, plays a crucial role in the system. In the continue we consider a non-canonical scalar field in general and we investigate the fixed point for the variety power ofaction. In the next part we find that the deceleration parameter and the fixed points are almost independent from parameter ( the power of the action). Also we will see that at two point the universegoes to the end with accelerated expansion which can describe the universe.
