Four falsehoods Giuliani spread about Dominion.

Dominion Voting Systems, one of the largest voting machine vendors in the United States, filed a defamation lawsuit against Rudolph W. Giuliani on Monday, accusing him of spreading a litany of falsehoods about the company in his efforts on behalf of former President Donald J. Trump to subvert the election.

The lawsuit chronicles more than 50 inaccurate statements made by Mr. Giuliani in the weeks after the election, and issues a point-by-point rebuttal of each falsehood. Here are four of the most common false statements Mr. Giuliani made about Dominion Voting Systems.

1. The Company’s Origin

Mr. Giuliani regularly stated, falsely, that Dominion “really is a Venezuelan company” and that it “depends completely on the software of Smartmatic,” a company “developed in about 2004, 2005 to help Chavez steal elections.”

As Dominion writes in its lawsuit: “Dominion was not founded in Venezuela to fix elections for Hugo Chávez. It was founded in 2002 in John Poulos’s basement in Toronto to help blind people vote on paper ballots.” The suit later adds that the headquarters for the company’s United States subsidiary are in Denver.

2. Programming Votes

Another often-repeated claim was that Dominion had programmed its machines to flip votes: “In other words when you pressed down Biden, you got Trump, and when you pressed down Trump you got Biden.”

This has been proved false by numerous government and law enforcement officials, including former Attorney General William P. Barr, who said in December: “There’s been one assertion that would be systemic fraud, and that would be the claim that machines were programmed essentially to skew the election results. And the D.H.S. and D.O.J. have looked into that, and so far, we haven’t seen anything to substantiate that.”

Similarly, a joint statement by numerous government and elections officials and agencies, including the National Association of State Election Directors, the National Association of Secretaries of State, and the Cybersecurity and Infrastructure Security Agency, stated that there was “no evidence that any voting system deleted or lost votes, changed votes, or was in any way compromised.”

The hand recount in Georgia also affirmed that the machine recounts were accurate in that state.

3. Antrim County, Mich.

Mr. Giuliani zeroed in on Antrim County, Mich., falsely claiming that a “Dominion machine flipped 6,000 votes from Trump to Biden” there, and that machines in the county were “62 percent inaccurate,” had a “68 percent error rate” and had an “81.9 percent rejection rate.”

Mr. Giuliani’s focus on Antrim County stems from human errors made by the county clerk on election night. According to the lawsuit, the clerk “mistakenly failed to update all of the voting machines’ tabulator memory cards.” But the suit says that “her mistakes were promptly caught as part of the normal canvass process before the election result was made official.” The Michigan secretary of state’s office also conducted a hand audit of all presidential votes in Antrim County that found the machines were accurate.

4. A Problematic Expert

Mr. Giuliani claimed that his accusations, particularly in Antrim County, were backed up by experts. But he largely relied on one man, Russell Ramsland Jr., a former Republican congressional candidate from Texas, who, according to the lawsuit filed by Dominion, had also publicly favored false conspiracy theories.

Dominion spent more than five pages on Mr. Ramsland’s lack of credentials to properly examine equipment, noting that he had a “fundamental misunderstanding of election software.” The suit also quotes the former acting director of the U.S. Election Assistance Commission Voting System Testing and Certification program, saying the report produced by Mr. Ramsland “showed a ‘grave misunderstanding’ of Antrim County’s voting system and ‘a lack of knowledge of election technology and process.’”