Answer by taking a quote from the following article:

Giuliani was born in an Italian-American enclave in East Flatbush in the New York City borough of Brooklyn, the only child of working-class parents, Harold Angelo Giuliani (1908-1981) and Helen Giuliani (nee D'Avanzo; 1909-2002), both children of Italian immigrants. Giuliani is of Tuscan origins from his father side, as his paternal grandparents (Rodolfo and Evangelina Giuliani) were born in Montecatini, Tuscany, Italy. He was raised a Roman Catholic. Harold Giuliani, a plumber and a bartender, had trouble holding a job, and was convicted of felony assault and robbery, serving time in Sing Sing.

Giuliani was prominent in the aftermath of the September 11 attacks. He made frequent appearances on radio and television on September 11 and afterwards--for example, to indicate that tunnels would be closed as a precautionary measure, and that there was no reason to believe that the dispersion of chemical or biological weaponry into the air was a factor in the attack. In his public statements, Giuliani said:  Tomorrow New York is going to be here. And we're going to rebuild, and we're going to be stronger than we were before... I want the people of New York to be an example to the rest of the country, and the rest of the world, that terrorism can't stop us.  The 9/11 attacks occurred on the scheduled date of the mayoral primary to select the Democratic and Republican candidates to succeed Giuliani. The primary was immediately delayed two weeks to September 25. During this period, Giuliani sought an unprecedented three-month emergency extension of his term from January 1 to April 1 under the New York State Constitution (Article 3 Section 25). He threatened to challenge the law imposing term limits on elected city officials and run for another full four-year term, if the primary candidates did not consent to the extension of his mayoralty. In the end leaders in the State Assembly and Senate indicated that they did not believe the extension was necessary. The election proceeded as scheduled, and the winning candidate, the Giuliani-endorsed Republican convert Michael Bloomberg, took office on January 1, 2002 per normal custom.  Giuliani claimed to have been at the Ground Zero site "as often, if not more, than most workers... I was there working with them. I was exposed to exactly the same things they were exposed to. So in that sense, I'm one of them." Some 9/11 workers have objected to those claims. While his appointment logs were unavailable for the six days immediately following the attacks, Giuliani spent a total of 29 hours over three months at the site. This contrasted with recovery workers at the site who spent this much time at the site in two to three days.  When Saudi Prince Alwaleed bin Talal suggested that the attacks were an indication that the United States "should re-examine its policies in the Middle East and adopt a more balanced stand toward the Palestinian cause", Giuliani asserted, "There is no moral equivalent for this act. There is no justification for it... And one of the reasons I think this happened is because people were engaged in moral equivalency in not understanding the difference between liberal democracies like the United States, like Israel, and terrorist states and those who condone terrorism. So I think not only are those statements wrong, they're part of the problem." Giuliani subsequently rejected the prince's $10 million donation to disaster relief in the aftermath of the attack.

What else was noteworthy about this time?
Giuliani claimed to have been at the Ground Zero site "as often, if not more, than most workers...