Count the total number of squares in a standard $4\times 4$ grid matrix configuration:

To find the total number of squares in an $n\times n$ square grid, we use the summation formula for the squares of natural numbers up to $n$:
$$\text{Total Squares}=\sum _{i=1}^n{i}^2=1^2+2^2+3^2+\cdots +n^2$$

For a $4\times 4$ grid ($n=4$):

* Number of $1\times 1$ squares = $4^2=16$
* Number of $2\times 2$ squares = $3^2=9$
* Number of $3\times 3$ squares = $2^2=4$
* Number of $4\times 4$ squares = $1^2=1$

$$\text{Total Squares}=16+9+4+1=30$$

The grid contains exactly $30$ squares.