Sorting algorithms are very popular fundamental algorithms in the field of computer science. Its job is sorting statistics so that they are arranged according to certain rules. In this paper, the kinds of sorting algorithms and their research method of them will be discussed. It will consist of discussing bubble sort, selection sorting, insertion sorting, hill sorting, and merge sorting. Those of them are that arrange a group of elements according to a certain number of ones. They are widely used in computer science and data processing in all walks of life. The most common sorting methods are numerical order and lexicographic order. Efficient sorting algorithms are significant in some of the algorithms, such as search and merge algorithms, so that they can arrive at the correct solution. Dealing with textual data and producing readable output are also important applications of sorting. The outcome is a permutation or recombination of the original input. So learning about the principles of those sorting algorithms by recognizing the code or reading pictures is significant. It is also necessary to be familiar with the applications of those algorithms which are beneficial to the daily life.