The document discusses the divide and conquer algorithm design paradigm and some examples of its applications. It describes divide and conquer as having three key steps: 1) divide the problem into subproblems, 2) solve the subproblems recursively, and 3) combine the solutions. It then lists several problems and their divide and conquer solutions, including merge sort, quick sort, calculating powers, randomized binary search, fast multiplication, finding maximum subarray sums, counting array inversions, and finding peak elements in an array.