public ReadOnlyObservableCollection<StandaloneTable> StandaloneTables {get;}

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

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

// this method finds a standalone table as a child of the map only
var table = aMap.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);
var map = MapView.Active.Map;//assumes non-null
QueuedTask.Run(() =>
{
  //move the first table to the bottom of the container
  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);
var map = MapView.Active.Map;//assumes non-null

QueuedTask.Run(() =>
{
  //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());
});