Can I have multiple primary keys in a single table?

Question

A Table can have a Composite Primary Key which is a primary key made from two or more columns. For example:

CREATE TABLE userdata (
  userid INT,
  userdataid INT,
  info char(200),
  primary key (userid, userdataid)
);

Update: Here is a link with a more detailed description of composite primary keys.

You can only have one primary key, but you can have multiple columns in your primary key.

You can also have Unique Indexes on your table, which will work a bit like a primary key in that they will enforce unique values, and will speed up querying of those values.

A table can have multiple candidate keys. Each candidate key is a column or set of columns that are UNIQUE, taken together, and also NOT NULL. Thus, specifying values for all the columns of any candidate key is enough to determine that there is one row that meets the criteria, or no rows at all.

Candidate keys are a fundamental concept in the relational data model.

It's common practice, if multiple keys are present in one table, to designate one of the candidate keys as the primary key. It's also common practice to cause any foreign keys to the table to reference the primary key, rather than any other candidate key.

I recommend these practices, but there is nothing in the relational model that requires selecting a primary key among the candidate keys.

This is the answer for both the main question and for @Kalmi's question of

What would be the point of having multiple auto-generating columns?

This code below has a composite primary key. One of its columns is auto-incremented. This will work only in MyISAM. InnoDB will generate an error "ERROR 1075 (42000): Incorrect table definition; there can be only one auto column and it must be defined as a key".

DROP TABLE IF EXISTS `test`.`animals`;
CREATE TABLE  `test`.`animals` (
  `grp` char(30) NOT NULL,
  `id` mediumint(9) NOT NULL AUTO_INCREMENT,
  `name` char(30) NOT NULL,
  PRIMARY KEY (`grp`,`id`)
) ENGINE=MyISAM;

INSERT INTO animals (grp,name) VALUES
    ('mammal','dog'),('mammal','cat'),
    ('bird','penguin'),('fish','lax'),('mammal','whale'),
    ('bird','ostrich');

SELECT * FROM animals ORDER BY grp,id;

Which returns:

+--------+----+---------+
| grp    | id | name    |
+--------+----+---------+
| fish   |  1 | lax     |
| mammal |  1 | dog     |
| mammal |  2 | cat     |
| mammal |  3 | whale   |
| bird   |  1 | penguin |
| bird   |  2 | ostrich |
+--------+----+---------+

(Have been studying these, a lot)

Candidate keys - A minimal column combination required to uniquely identify a table row.
Compound keys - 2 or more columns.

• Multiple Candidate keys can exist in a table.
  • Primary KEY - Only one of the candidate keys that is chosen by us
  • Alternate keys - All other candidate keys
    • Both Primary Key & Alternate keys can be Compound keys

Sources:
https://en.wikipedia.org/wiki/Superkey
https://en.wikipedia.org/wiki/Candidate_key
https://en.wikipedia.org/wiki/Primary_key
https://en.wikipedia.org/wiki/Compound_key