In this paper, five different sorting methods will be discussed. Each method will be analyzed and discussed in detail pointing out its efficiency, weaknesses, powerfullness, and the appropriate type of applications. The different methods are represented graphically using Turbo Pascal where one pass is performed in each method at a time. The methods discussed in this project are, Bubble Sort, Quick Sort, Heap Sort, Shell Sort, and Double Selection Sort. The latter is a new method that I modified from the Selection Sort. Finally, comparisons between the sorting methods mentioned above will be discussed.