How many rectangles are there in the chessboard?

A standard chessboard has $8$ rows and $8$ columns, which means there are $9$ horizontal grid lines and $9$ vertical grid lines.
To form any rectangle (including squares), we need to choose $2$ horizontal lines out of $9$ and $2$ vertical lines out of $9$.

The number of ways to select $2$ horizontal lines from $9$:

$${}^9{C}_2=\frac{9\times 8}{2\times 1}=36$$

The number of ways to select $2$ vertical lines from $9$:

$${}^9{C}_2=\frac{9\times 8}{2\times 1}=36$$

The total number of rectangles is the product of these selections:

$$\text{Total Rectangles}={}^9{C}_2\times {}^9{C}_2=36\times 36=1296$$