Suppose $A$ is a central simple algebra over a field $F$, $\mathcal{O}_F$ is an integrally closed subring of $F$ and suppose $\mathcal{O}_F$ is noetherian. Then an order of $A$ is a $\mathcal{O}_F$ lattice of $A$, stable under the algebra operations. In this case, the maximal order always exists. My questions:

Are there some nontrivial criterion for an order being maximal? And how to construct a maximal order starting from a given order? (I only know the existence from some ACC argument)

In fact, what I really concern is why we could always find a maximal order stable under a given involution on $A$.

Any hint is welcome! Thanks.