

The United Federation of Planets was formed in the Earth calender year 2161, on May 8th. Admiral Eugene Roddenberry declared this day to be the day that the Earth made a new alliance that would spread the word of peace and exploration across the universe.
Humans, Vulcans, Tellarite, Andorians and the Centauri colonies jointly formed the first member races of the United Federation of Planets. A constitution was drawn up, much in the vein of the 1776 constitution of the United States of America. A new age of peace and prosperity was born, and the expansion into the stars increased at a logarithmic rate. Co-operation between Federation member races increased, advancing technology forwards in all aspects. New races with warp technology were signed up to the Federation.
The Federation consists of:
Supreme Assembly
Federation Council
Economic and Social Council
Trusteeship Council
Interplanetary Supreme Court of Justice
Starfleet
Secretariat
The Federation is overseen by a democratically elected President. The Presidency of the U.F.P. is based upon four year terms. Presidents may be elected for more than one term of office, but for no more than two terms under normal circumstances.

As can be seen from the above breakdown of the Federation, Starfleet is the exploratory and defensive organisation of the Federation and is thus ultimately controlled by the democratically elected members of the Federation Council and the President has final authority over Starfleet matters.
Currently, as of Stardate 11202.5, the United Federation of Planets consists of 105 members, covering an area of space that requires several months at high warp speeds to cover from end to end. Earth is the administrative headquarters of the Federation, with the President's office based in Paris, France, and the Federation Council based in San Francisco, near to the Starfleet Command buildings. The Federation is also responsible for numerous colony worlds.
Author's Notes:
The United Federation of Planets is something that requires discussion in quite a bit of detail. So it's cup of tea time and a comfy chair before you read further.
The first thing to point out about the United Federation of Planets that maybe isn't stressed enough in the show is the aspect that the Federation is an ideal. This ideal, when examined, is focussed on the major homeworlds of the Federation members, and is spread outwards through the administrative aspects of the Federation, such as embassies, ambassadors and, most importantly, Starfleet. Starfleet officers and personnel are taught the ideals of the Federation and go forth into the stars to practice these ideals and uphold these same ideals no matter what is faced.
Federation media is also a powerful tool for the spreading of the Federation ideal. As Quark and Garak noted in Deep Space Nine, the Federation is insidious. The Federation ideal is a very attractive one, peace and prosperity, sharing of knowledge and the light of no longer possessing the chains of money and wealth to burden our desires with. Of course, as with most [if not all] ideals, the ideal is most strongest at the source, and the further away from the source one travels, the less strong this ideal is. It is easy to imagine paradise on Earth. All poverty and disease has been defeated, pollution and starvation are the nightmares of the past, and everyone has the equal opportunity to achieve anything they desire and be anything they desire. Further outwards, on the outer rims of the Federation, where supplies are stretched to the limit, where many of the technological advances have not yet reached, these dreams and ideals seem almost as far away as they do in present day Earth.
That isn't to say that the original dreams of Gene Roddenberry do not reach out beyond the core systems. It is just to say that the message and the dream is still spreading out from the homeworlds, like ripples in a pond. One example of this Nimbus III, the Planet of Galactic Peace. As shown in Star Trek V, despite the ideals of the Federation, and the best intention in the Universe, sometimes dreams take a little longer to come to fruition. despite the best intentions of the Federation, resources are not infinate. Many of the colonies shown in the Original Series also show Federation colonies [such as the ones visited by Mudd's Women] to still be of a basic nature, where the colony exists to supply dilithium to power the dreams of the Federation.

Starbase 77 is another example of where intentions and ambitions have yet to gel together.
The Federation is still going through a period of growth, and growth is painful. Picard's Federation is still 70 years away, and the message that will eventually permeate the Federation is still spreading outwards, like bubbles in a soft drink. The dream will be realised, it is only a matter of time.
The name Admiral Eugene Roddenberry has often been cited in very small print on starship plaques since the time of Star Trek: The Next Generation. It is only right that Gene Roddenberry have his mention is Star Trek history. This is, after all, his vision that he has shared with us all.
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