What is the formulation of linear transform from $\mathbb{R}^{m \times n} \to \mathbb{R}^{p}$

I knew that a linear transform from $\mathbb{R}^m \to \mathbb{R}^{p}$ can be presented as a $p\times m$ matrix. So, I think that a matrix from $\mathbb{R}^{m \times n} \to \mathbb{R}^{p}$ likes a notebook whose each its page is a $m \times n$ matrix. But if it is true, then how can I present that matrix.

The answer depends (in a sense) on how you are representing elements of $\mathbb{R}^{m \times n}$. If they are just $m \times n$ tuples then you have a $p \times mn$ matrix.

If you are thinking about those elements as matrices themselves then you choose a basis $B$ of the space of matrices - probably the $m\times n$ matrices each of which has a single $1$ entry with the rest $0$. Then the matrix of your linear transformation has $p$ rows indexed $1, \ldots, p$ and $m \times n$ columns indexed by the elements of $B$.