[Solution] Obviously, each square that meets the requirements of the problem is uniquely determined by its side length and the vertex at its lower left corner. For a square with side length $k(k=1,2, \cdots, 9)$, its lower left vertex must lie on the nodes of the $(9-k) \times(10-k)$ rectangle in the lower left of the given rectangle. The number of these nodes is $(10-k)(11-k)$. Therefore, the total number of squares that meet the requirements is
$$
S=\sum_{k=1}^{9}(10-k)(11-k)=420 .
$$
1.80 Given a $9 \times 10$ rectangular grid paper where each small square has a side length of 1. Using the grid points as vertices and the grid lines as edges to form squares, how many such squares can be formed?