Although the area in which it is situated was first claimed for France by Rene Robert Cavalier, Sieur de La Salle, New Orleans itself was founded in 1718 by Jean Baptiste La Moyne, Sieur de Bienville, intended to both secure France's strategic command of the Mississippi River and to function as a capital of the province of Louisiana (named for King XIV and his wife Queen Anne).
Initial development of the city was difficult, an indication of the many problems New Orleans would face throughout its history: it is not easy to build a city in a swamp, especially a swamp that is twenty feet below sea level, requiring levees all around it and sinking a few inches a year.
Nonetheless, New Orleans was built in the fashion of European city, with distinct quarters and narrow, pedestrian streets, French architecture and names, and the generally labyrinthine atmosphere of the Old World. Though France's mercantilism was problematic for its colonies, New Orleans grew at a steady rate, and was perhaps the only city in the South which actually posessed an aristocracy (albeit a debauched, depraved, and generally incompetent one).
In 1763, France's economic situation was grim, and its defeat in the Seven Years War necessitated the auctioning of several territories, including Louisiana. New Orleans was sold to Spain, and although the French settlers were somewhat unhappy with this transaction (that's another node entirely), the period which followed saw the growth of the city's economy and the advent of a new, more distinct cultural identity.
Though France eventually regained control of Louisiana, they sold it almost immediately to the United States in a deal for $40 million dollars. The Louisiana Purchase garnered America land from the Mississippi River almost all the way to the Pacific Ocean, and was considered a superlative achievment for President Thomas Jefferson.
As an American city, New Orleans grew in population to 170,000, behind only New York and Baltimore. The local economy exploded, as well, with the introduction of the steam boat, the cotton trade, and the sugar cane trade. During the nineteenth century, New Orleans' many disparate neighborhoods began to acquire distinct identities: the French Quarter, the Garden District, the Faubourg Marigny, Uptown, and the Irish Channel all became specific miniature cities, with their own cultural and social traditions, which fused together to provide New Orleans with an utterly inimitable urban personality. Mardi Gras, which had been enacted for a century, grew into a larger phenomenon as well, with all manner of parades for the city's many different demographic groups: African Americans, the Irish, French, Spanish, and British whites, the Cajuns, and the Creoles all had their own organizations, and the festival began to define a large portion of the city's social structure.
The Civil War had relatively little impact on New Orleans; the city's participation was minimal, and, as a result, the punitive measures enacted on New Orleans afterward were negligible. The end of slavery was also a comparatively minor event in the city, as its economy was mercantile, rather than agricultural. The very slight degree to which Reconstruction affected the city was a major factor in New Orleans' race relations; whereas in other parts of the South, whites resented blacks for the social changes brought about after the Civil War, in New Orleans these changes were rather mild, and a century later, the Civil Rights movement encountered less opposition in the Crescent City than it did elsewhere.
New Orleans is now a major metropolitan area, complete with suburbs, over two million residents, and a major (if struggling) economy. Analyses of the distinct cultural, racial, and social elements of the city, and their possible basis in its historical and economic heritage, belong in other nodes, which I will hardlink as they are written.
And if you have something you'd like linked here, feel free to /msg me. I'd love to add much more to this write-up.
Neighborhoods:
---French Quarter
---Faubourg Marigny
---Garden District
---Irish Channel
Residents
---Walker Percy
---Anne Rice
---Truman Capote
---Louis Armstrong
---The Marsalis Family
---William Faulkner
As Gritchka helpfully mentioned, I've written an entire node about New Orleans without any significant reference to jazz. Until I can add more, check out Sidney Bechet, Louis Armstrong, Congo Square, and general nodes concerning jazz.
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Mercuryblues has noted a number of factual errors within my original w/u, as well as several errors of omission, which I will include here as Mercuryblues sent them to me:
"There is no real Cajun population here in New Orleans. Any Cajuns here were assimilated into the local (different) French culture... While the Civil War didn't impact New Orleans too too much, New Orleans had an ENORMOUS impact on the Civil War. The city at that time was the second largest port in the US, and when it was taken (with little defenses becuase most of the men were off fighting in the Army of Northern Virginia), this pretty much sealed the South's fate in the Civil War.
Also, you left out a huge immigrant group - the Italians. There was never a significant Spanish population compared to others though the city was under spanish administration and that's why the predominant style of architecture in old New Orleans is Spanish (the city was burned down many times so the French stuff is mostly gone).
Some other important people are John Kennedy O'Toole, Fats Domino, Ernie K-doe, Jean Lafitte (for the most part), Better Than Ezra, Cowboy Mouth, and many many more... Also the neighborhoods Mid-City, 9th Ward, 7th Ward, Carrolton, Faubourg St. Martin, Bywater, Warehouse District, Bucktown, Lakeview, New Orleans East, also the traditional name for the French Quarter is the Vieux Carre..." | 
