Differential rotation plays a key role in providing toroidal magnetic field from the poloidal one for solar activity. It is generally agreed that the Sun's differential rotation drives the solar dynamo for generating all solar activity. However, the role of the differential rotation as a participant in the cycle of magnetic activity variation is not yet clear. Hence, study of the variations of differential rotation during the solar cycle and its north-south asymmetry is essential for understanding the mechanism of the solar cycle, the Sun's internal dynamics and the variations in the solar magnetic activity, as well as for finding the cause of the variations in the differential rotation. In chapter one, on the base of surveying a number of references, we summarized the basic knowledge of solar surface differential rotation. The history of the study of solar rotation, the two basic methods used in investigating the solar rotation rate and some important research results of the solar rotation are introduced first. Then some main results of temporal variation of solar rotation are reviewed including the long-term variation, the solar-cycle dependent, the periodicity and the north-south asymmetry. Finally, some theories study for what cause the differential rotation and what maintains it are summarized simply. In chapter two, the daily sunspot numbers of the whole disk as well as the northern and southern hemispheres from 1945 January 1 to 2010 December 31 are used to investigate the temporal variation of rotational cycle length through the continuous wavelet transformation analysis method. The main results are listed as follows： 1. Auto-correlation function analysis of daily hemispheric sunspot numbers shows that the southern hemisphere rotates faster than the northern hemisphere. 2. The results obtained from the wavelet transformation analysis are that no direct relationship exists between the variation trend of the rotational cycle length and the solar activity in the two hemispheres. 3.The rotational cycle length of both hemispheres has no significant period appearing at 11 yr, but has a significant period of about 7.6 yr. 4.Analysis concerning the solar cycle dependence of the rotational cycle length shows that acceleration seems to appear before the minimum time of solar activity in the whole disk and the northern hemisphere, respectively. 5.Furthermore, the cross-correlation study indicates that the rotational cycle length of the two hemispheres has different phases, and that the rotational cycle length of the whole disk as well as the northern and southern hemispheres, also has phase shifts with corresponding solar activity. 6. the temporal variation of the north-south (N-S) asymmetry of the rotational cycle length is also studied. This displays the same variation trend as the N-S asymmetry of solar activity in a solar cycle, as well as in the considered time interval, and has two significant periods of 7.7 and 17.5 yr. Moreover, the rotational cycle length and the N-S asymmetry of solar activity are highly correlated. It is inferred that the northern hemisphere should rotate faster at the beginning of solar cycle 24. In the last chapter, some unsolved questions about the solar differential rotation are given and what I can do to further my study in the next stage are presented.
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