The Quicksort Algorithm is a highly efficient, comparison-based sorting algorithm that uses the divide-and-conquer strategy to sort elements in an array or list. It is one of the fastest and most widely used sorting algorithms, particularly favored for its average time complexity of O(n log n), making it suitable for sorting large datasets.

Quicksort works by selecting a pivot element from the list and partitioning the other elements into two sub-arrays: those that are less than the pivot and those that are greater. The pivot element is then placed in its correct position, and the process is recursively applied to the sub-arrays. This recursive partitioning continues until the entire list is sorted.

One of the key advantages of Quicksort is its ability to perform well on average, even though its worst-case time complexity is O(n²), which occurs when the pivot element consistently divides the array into highly unbalanced partitions. This can be mitigated by choosing the pivot element randomly or by using a median-of-three method. Quicksort is particularly efficient for in-place sorting and is commonly used in applications like database indexing, file organization, and system-level sorting tasks.