Introduction:
An AVL tree is a self-balancing binary search tree where the heights of the left and right subtrees of any node differ by at most 1. The height of a tree is defined as the maximum number of edges in any path from the root to a leaf node. In this question, we are given that the AVL tree has 7 nodes and we need to determine its maximum height.

Explanation:
To find the maximum height of an AVL tree with 7 nodes, we can consider the minimum number of levels required to accommodate these nodes. Since AVL trees are balanced, the minimum number of levels can be achieved by having the maximum number of nodes at each level.

Step 1: Finding the number of nodes at each level:
To distribute 7 nodes across the levels, we can start with the root level and distribute nodes in a balanced manner. The number of nodes at each level can be determined using the following pattern:

Level 1: 1 node (root level)
Level 2: 2 nodes
Level 3: 4 nodes
Level 4: 7 nodes (remaining 7 nodes)

Step 2: Calculating the height:
To calculate the height of the AVL tree, we need to find the maximum number of levels required to accommodate the given number of nodes. In this case, the maximum number of levels needed is 4, which corresponds to Level 4 in the distribution pattern above.

Therefore, the maximum height of the AVL tree with 7 nodes is 4.

Conclusion:
In summary, the maximum height of an AVL tree with 7 nodes is 4. This is achieved by distributing the nodes across the levels in a balanced manner, ensuring that the heights of the left and right subtrees of each node differ by at most 1.