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Abstract The aim of the thesis is to review the accelerating expansion of the universe and its contradiction with predictions of the general theory of relativity. The many successes of the theory in explaining cosmo- logical phenomena are reviewed. The history of the expansion of the universe is also discussed and suggested solutions for the problem of the accelerating expansion of the Universe are explored. Advantages and disadvantages of each solution are reviewed. A geometric uni{uFB01}ed {uFB01}eld theory in absolute parallelism is formulated. It is shown that the new theory satis{uFB01}es the limits of the general theory of relativity |