Glossary
Here are some terms that are used when discussing AVL trees:

child  same as for binary search trees

parent  same as for binary search trees

leaf  same as for binary binary search trees

grandparent  parent of parent

favorite the child who roots the taller subtree 
if the parent's balance factor is 1, the left child is the
favorite 
if the parent's balance factore is 1, the right child is
the favorite 
if the parent's balance factor is 0, no child is the favorite

linear  true if the parent and child are both left children or
are both right children

rotation  make a child a parent and the former parent a child
 preserves binary search tree ordering
Note that terms like
favorite and linear
are not found in other AVL search tree
descriptions.
They are used here in order to remove leftness and rightness issues from the main
AVL tree algorithms.
AVL properties
An AVL tree has the following properties:

Leaves have a balance factor of zero

Interior nodes have a balance factor of 1, 0, or 1
The balance factor marks which child is the root of the taller
subtree and is computed by subtracting the height of the right child's
subtree from the height of the left child's subtree. This means that
an AVL tree is nearly as balanced as it can be with just a little
bit of slop allowed.
Redblack trees,
on the other hand, allow a good deal more slop with regards to
balance.
Next:
Inserting into AVL trees