QUICK-SORT
Quick-sort is very fast, pedagogically important, and challenging to understand.
Check out the simplest way to partition the array, while still in-place.
MERGE-SORT
Merge-sort is very fast, and its only downside is that it is typically not in-place.
See why it has a guaranteed worst-case time complexity of O(n log n).
INSERTION-SORT
A simple algorithm that is more efficient in practice for small arrays than asymptotically better algorithms.
Understand how and why it works in O(n²).
BUBBLE-SORT
Even if better sorting algorithms exist, bubble-sort is still interesting to study and is pedagogically relevant.
Check out the lesser-known reason of why exactly it terminates.
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BINARY SEARCH
Binary search is absolutely fascinating. It is one of the few algorithms that is faster than the size of the input.
Understand how it works, how to implement it, and why it is so fast.