As already said, if you modify the contents of the
same datatable in another window the datagridview binded to that datatable will be updated.
If you want to do programmatic operations, one way that you add a new event in the frmNewBook, for example:
public event System.Action NotifyAnotherForm;
Now when you create the form you wire that event:
frmNewBook a = new frmNewBook();
a.NotifyAnotherForm += new System.Action(a_NotifyAnotherForm);
a.Show();
In the main form you have the method that handles the event, something like:
void a_NotifyAnotherForm() {
custom code goes here
}
And when you do modifications in the frmNewBook, you raise the event in proper place:
if (NotifyAnotherForm != null) {
NotifyAnotherForm();
}