This lecture covers the importance of sorting methods in practice, as they are essential for efficient searching and are used in various algorithms. It explains the problem of sorting, differentiates between sorted and unsorted data, and introduces the concept of internal sorting. The lecture presents the insertion sort algorithm, detailing its simple principle and step-by-step execution. It also explores various sorting algorithms such as selection sort, shell sort, quick sort, and heap sort, comparing their complexities and practical performance. The lecture concludes with insights on when sophisticated sorting methods outperform simple ones, highlighting the efficiency of quick sort and the limitations of bubble sort.