public ReadOnlyObservableCollection<StandaloneTable> StandaloneTables {get;}

{
    // these routines find a standalone table whether it is a child of the Map or a GroupLayer
    var tblFind = map.FindStandaloneTable("CIMPATH=map/address_audit.xml");

    IReadOnlyList<StandaloneTable> tables = map.FindStandaloneTables("addresses");

    // this method finds a standalone table as a child of the map only
    var table = map.StandaloneTables.FirstOrDefault(t => t.Name == "Addresses");
}

{
    var container = MapView.Active.Map;

    //the map standalone table collection
    var table = container.GetStandaloneTablesAsFlattenedList()
                            .FirstOrDefault(tbl => tbl.Name == "EarthquakeDamage");

    //or from a group layer
    var grp_layer = MapView.Active.Map.FindLayers("GroupLayer1").First() as GroupLayer;
    var table2 = grp_layer.FindStandaloneTables("EarthquakeDamage").First();
    //or         grp_layer.GetStandaloneTablesAsFlattenedList().First()
    //or         grp_layer.StandaloneTables.Where(...).First(), etc.

    //show the table in a table view 
    //use FrameworkApplication.Current.Dispatcher.BeginInvoke if not on the UI thread
    FrameworkApplication.Panes.OpenTablePane(table2);
}

{
    //get the first group layer that has at least one table
    var grp_layer = MapView.Active.Map.GetLayersAsFlattenedList()
      .OfType<GroupLayer>().First(g => g.StandaloneTables.Count > 0);
    grp_layer.MoveStandaloneTable(grp_layer.StandaloneTables.First(), -1);

    //move the last table in the map standalone tables to a group
    //layer and place it at position 3. If 3 is invalid, the table
    //will be placed at the bottom of the target container
    //assumes the map has at least one standalone table...
    var table = map.StandaloneTables.Last();
    map.MoveStandaloneTable(table, grp_layer, 3);

    //move a table from a group layer to the map standalone tables
    //collection - assumes a table called 'Earthquakes' exists
    var table2 = grp_layer.FindStandaloneTables("Earthquakes").First();
    //move to the map container
    map.MoveStandaloneTable(table2, 0);//will be placed at the top
}

{
    //get the first group layer that has at least one table
    var grp_layer = MapView.Active.Map.GetLayersAsFlattenedList()
      .OfType<GroupLayer>().First(g => g.StandaloneTables.Count > 0);

    //Note: Run within a QueuedTask
    //get the tables from the map container
    var tables = map.GetStandaloneTablesAsFlattenedList();
    //delete the first...
    if (tables.Count() > 0)
    {
        map.RemoveStandaloneTable(tables.First());
        //or delete all of them
        map.RemoveStandaloneTables(tables);
    }

    //delete a table from a group layer
    //assumes it has at least one table...
    grp_layer.RemoveStandaloneTable(grp_layer.StandaloneTables.First());
}