There are many other sorting algorithms, each with different characteristics and trade-offs. Some of the common ones are:

Selection Sort: A simple algorithm that repeatedly finds the minimum element in the unsorted part of the array and puts it at the end of the sorted part. It has a time complexity of O(n^2) and is not stable.
Bubble Sort: A simple algorithm that repeatedly swaps adjacent elements that are out of order until the array is sorted. It has a time complexity of O(n^2) and is stable.
Insertion Sort: A simple algorithm that builds the sorted array one element at a time by inserting each element into its correct position. It has a time complexity of O(n^2) and is stable.
Merge Sort: A divide-and-conquer algorithm that recursively splits the array into two halves, sorts each half, and then merges them back together. It has a time complexity of O(n log n) and is stable.
Quick Sort: A divide-and-conquer algorithm that partitions the array around a pivot element, such that all elements smaller than the pivot are on its left and all elements larger than the pivot are on its right, and then recursively sorts each subarray. It has an average time complexity of O(n log n) but a worst-case time complexity of O(n^2). It is not stable by default but can be made stable with some modifications.
Heap Sort: An algorithm that uses a binary heap data structure to efficiently find and remove the maximum element from the unsorted part of the array and append it to the sorted part. It has a time complexity of O(n log n) and is not stable.
Some of the problems that Heap Sort solves are:

It can sort an array in-place, using only O(1) extra space.
It can handle large datasets efficiently, as it has a good asymptotic time complexity.
It can be easily parallelized, as each heap operation can be performed independently.
Some of the problems that Heap Sort does not solve are:

It does not preserve the relative order of equal elements, as it is not stable.
It does not have good cache performance, as it accesses elements that are far apart in memory.
It does not perform well on nearly sorted or reverse sorted arrays, as it does not take advantage of existing order.
I hope this answers your question.
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