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The Federation Starfleet, more commonly known as Starfleet, was the military and exploratory arm of the United Federation of Planets.
Starfleet was founded in 2161 after the Articles of Federation was signed. Starfleet was initially comprised of the United Earth Starfleet, the MACOs, and the space forces of the other founding worlds, such as the Andorians, Vulcans, and Tellarites. In addition to keeping the new nation secure from aggressive neighbors like the Klingons and Orions, they also helped monitor the Romulan Neutral Zone.
Initially using the equipment from the predecessor forces, Starfleet soon began designing its own ships and equipment, borrowing most heavily from United Earth designs as those were the most versatile.
Over the next century the Federation had only sporadic contact with the heavily fractured Klingon Empire, and no contact with the Romulans - who were content to remain within their borders and rebuild their strength after the Earth-Romulan war.
In the 2240s the Federation launched the Constitution class starships. Ships of this class - such as the USS Enterprise (NCC-1701) - played a major role in exploring the galaxy and defending the Federation.
The Klingons reunited their 24 Great Houses thanks to the efforts of T'Kuvma, and engaged the Federation in a war in 2256. The war did not go well for the Federation, with Starfleet losing 1/3 of their fleet by the time the Klingons ceased hostilities in mid 2257.
After the war, in addition to various ground and space based installations, Starfleet had approximately 7,000 ships in 2257.
In the 2260s the Romulans re-emerged from their self imposed isolation, and entered the galactic political scene as they probed Starfleet to see if they could successfully engage in a new war with the Federation.
In the latter half of the 23rd century officers such as Captain James T. Kirk and Commander Spock contributed a great deal in not only defending the Federation, but in expanding its influence through diplomacy with other civilizations.
The early to mid 24th century was a period of relative peace and stability in the galaxy, with the Klingons setting aside their differences with the Federation and the Romulans keeping within their own borders. In 2364 the Romulans renewed their presence in the galaxy, challenging Starfleet's new Galaxy class starships such as the Enterprise-D with their D'Deridex class warbirds.
The late 24th century was a difficult time for the Federation Starfleet. In the 2370s the Cardassians allied themselves the Dominion. The Dominion and their Cardassian allies soon engaged the Federation and Klingons in a devastating war. The Romulans also joined the alliance against the Dominion due to manipulation by Captain Benjamin Sisko that convinced them the Dominion assassinated a high ranking Romulan Senator. The Dominion War came to an end in 2375 when the Federation pushed the Dominion back to Cardassia and Female Changeling was talked into surrendering by Odo. All of the allies suffered major damage, but the Cardassians took the brunt of the casualties, with over 800 million dead by the end of the war.
A few years later, in 2381, the Borg invaded the Federation. A number of Federation worlds were devastated in the attack, and nearly half of Starfleet was destroyed by the time the Caliear intervened and stopped the Borg. Following the invasion of 2381 the Federation decided Starfleet needed to get back to return to its roots as an organization dedicated to exploration of the galaxy, and sent ships such as the Enterprise-E out to explore the galaxy.
Over the years Starfleet had members from a large number of species throughout the Alpha Quadrant. These included Humans, Androids, Vulcans, Tellarites, Andorians, Klingons, Ferengi, Betazoids, Bajorans, Triexians, Rigellians, Betelgeusians, Cardassians, Caitians, Saurians, and Bolians.
By the late 24th century, Earth born humans were in a minority on some Starfleet vessels, with such ships either being crewed by humans from other worlds or by aliens. The Titan was a ship with a very diverse crew, with humans and both humanoid and non humanoid aliens on the ship.