Finding contiguous ranges in grouped data
Since MySQL doesn't support ROW_NUMBER(), You can use a variable to create a group like this.

Sample Data

CREATE TABLE `Rings` (
    ID_RingType CHAR(2),
    Number MEDIUMINT UNSIGNED,
    ID_User INT(11)
);

INSERT INTO `Rings` VALUES
  ('AA',1,1),
  ('AA',2,1),
  ('AA',3,1),
  ('AA',11,1),
  ('AA',12,1),
  ('AA',13,1),
  ('AA',14,1),
  ('AA',15,1),
  ('AB',16,1),
  ('AB',17,1),
  ('AB',18,1),
  ('AB',19,1),
  ('AB',20,2),
  ('AB',21,2),
  ('AB',22,2);


Query

SET @grp = 0;
SET @preNum = 0;

SELECT ID_User,ID_RingType,MIN(Number),MAX(Number) FROM
(
SELECT 
ID_RingType,
ID_User,
Number,
@grp := CASE WHEN Number = @preNum + 1   THEN @grp ELSE @grp + 1 END grp,
@preNum := Number 
FROM `Rings`
ORDER BY ID_RingType,ID_User,Number
)T
GROUP BY ID_RingType,ID_User,grp


Output

ID_User | ID_RingType | MIN  | MAX
1       | 'AA'        | 1    | 3
1       | 'AA'        | 11   | 15
1       | 'AB'        | 16   | 19
2       | 'AB'        | 20   | 22