Sorting is one of the most fundamental problems in computer science. In this work, some sorting algorithms are studied. We discussed these algorithms taking into account the technique, the general form, and the analysis for each algorithm. Measures of presortedness are also given. A new sorting algorithm is developed. By considering the time as a measure of efficiency, it is shown that the new algorithm is more efficient than the Bubblesort, the Insertionsort, the Shellsort, merge sort, and the Selectionsort algorithms. The Quicksort technique is still the most efficient algorithm for sorting. Future work of this paper is also given.