Short answers, pulled from the story.
Tammany Hall was founded in 1786 and formally incorporated as the Tammany Society on the 12th of May, 1789. It was dissolved in 1967, after nearly 178 years of operation in New York City politics.
William M. Tweed, known as "Boss" Tweed, is the most notorious leader in Tammany history. His ring doubled the state debt from $50 million to $113 million over two years before his arrest in 1872 and conviction for corruption. He died in Ludlow Street Jail in 1878.
Tammany Hall provided Irish immigrants with patronage employment, job referrals, legal aid, food, shelter, and citizenship and naturalization services. By 1855, Irish immigrants composed 34 percent of New York City's voter population, and Tammany secured their votes by acting as a social welfare organization before formal government programs existed.
The Tweed ring collapsed after county auditor James Watson was fatally injured in a sleigh accident on the 21st of January, 1871, and his financial records were subsequently handed to The New York Times. Harper's Weekly and the editorial cartoons of Thomas Nast intensified public pressure, and a Committee of Seventy formed at a Cooper Union mass meeting on the 4th of September led to Tammany's defeat in the 1871 city elections.
Carmine DeSapio, Tammany's first Italian-American boss, led the organization from 1949 to 1962. He was ousted as Greenwich Village district leader by a reform coalition and was subsequently defeated in bids to reclaim that post in 1963 and 1965 by Ed Koch, leader of the Village Independent Democrats.
La Guardia reorganized city government with non-partisan officials, adopted a new city charter in 1936 that abolished the ward system underpinning machine politics, and increased civil service examinations to cover roughly three-quarters of city positions by 1939, up from about half in 1933. He also became the first anti-Tammany mayor to win re-election, defeating Jeremiah T. Mahoney in 1937.