Founded: 2161 
Members: 150+ 
Also Known As: The Federation 
Location: Alpha Quadrant 
Headquarters: San Francisco, Earth 
Prominent Members: Humans, Vulcan's, Trills, Deltan's, Andorians, Betazoids. 

Right A Picture of the President's Office of the United Federation Of Planets, Paris Earth.
The United Federation Of Planets was founded in 2161, in the aftermath of the Romulan wars.  It has a constitution that seeks mutual scientific, diplomatic, and cultural benefits for its members.  It also guarantees important protections to sentient beings, including the Seventh Guarantee, which prevents a citizen against self-incrimination.  The Federation is 150 plus strong in members, these include planets, colonies, and other political units.  Anyone aboard Federation ships or on Federation Planets come under the protection of the constitution.  The Federation wa designed to help all members, and is no doubt a major force in the Galaxy, and has prevented many interstellar battles.  Any planet may apply to become a member of the Federation, but it is a process that takes several years.  To qualify the planet must for fill these basic requirements. They must have a peaceful world government, political stability, and must provide their citizens with a number of basic rights.
Starfleet is the Federation's authority for the operation of interstellar and galactic exploration and defense,  It was founded in the same year as the Federation.  It is designed to expand knowledge of all Federation Planets and its motto is "ExAstris, Scientia", or "From the stars, knowledge".
Starfleets mission is to seek out new life, and boldly go where no-one has gone before.  All ships under the command of Starfleet must follow a set of guidelines which are called the Prime Directive.  This stops any Starfleet ship or Officer interfering in the normal development of any society or planet, even if this interference is believed to be the right thing to do.