You learn binary search trees and walk away believing every operation is O(log n). It isn't. That guarantee only holds when the tree stays balanced, and a plain BST has no mechanism to enforce that. Insert [1, 2, 3, 4, 5] into an empty BST and you've built a linked list with extra steps.
TL;DR: An AVL tree adds one rule to a BST. No node's left and right subtrees can differ in height by more than 1. When an insertion breaks the rule, the tree fixes itself through rotations. Every operation stays O(log n). The four rotation cases aren't four separate things to memorise. They're two atomic moves combined twice.
The balance rule everything else hangs on
An AVL tree is a self balancing BST where, for every node, the heights of its left and right subtrees differ by at most 1. That's the whole rule. Every operation that preserves the rule preserves O(log n).
You track the rule with the balance factor:
