Some more 4-1-1 on the Shire: it is divided into four parts (North, South, West, and East), with later additions of Buckland and the Westmarch.
There has been no king in the Shire for over a thousand years, although they do have a leader, the Thain. In general, the Thain of the Shire has come from the prominent Took family.
Supposedly, the Thain runs the Shire militia, but it's mainly a ceremonial title at this point, since it's been so long since the Shire needed armed protection. That's good news.
As of this age, the only real official in the Shire is the Mayor of Michel Delving (or of the Shire), who is elected every seven years.
The closest thing the Shire has to a police force are its Shirriffs. (Not to be confused with sheriffs.)
They also employ a number of Bounders to keep an eye on the boundaries of the Shire and make sure that no weird Outsiders are trying to get in. Outsiders... spooky.
By the time the The Fellowship of the Ring starts, the number of Bounders has been increasing. No one has figured out what this rising need for patrolling the boundaries might mean (not even the Shire's one adventurer, Bilbo Baggins).
It's been sixty years since Bilbo came back from his quest. Heis rich and has still kept his magic ring a secret.
In the meantime, he has also grown close to a favorite nephew of his, Frodo Baggins.