Explainer: From Syria to Bill's women - The claims and the facts from the US presidential debate
HERE is an analysis of some of the claims made in the second presidential debate.
DONALD TRUMP on women linked to Bill Clinton sexually: "Hillary Clinton attacked those same women and attacked them viciously."
THE FACTS: There is not clear, independent evidence that Hillary Clinton "viciously" attacked women who alleged or confirmed sexual contact with her husband.
To be sure, in the 1992 Democratic primaries, she was deeply involved in the Clinton campaign's effort to discredit one accuser, actress Gennifer Flowers, who alleged she had a long-running affair with Bill Clinton. Both Clintons acknowledged past troubles in their marriage but sought to undermine Ms Flowers' claims. Bill Clinton later acknowledged in a 1998 court deposition that he had a sexual encounter with Ms Flowers.
Hillary Clinton was also quoted over the years making disparaging comments about other women linked with her husband, but what is lacking is proof that she engineered efforts to smear their reputation.
Diane Blair, a political science professor and long-time Hillary Clinton friend who died in 2000, left behind an account of private interviews with Mrs Clinton in which she told her during the Monica Lewinsky affair that she considered the former White House intern a "narcissistic loony toon".
DONALD TRUMP on Mrs Clinton's behaviour when, as a young defence lawyer, she was assigned to represent an accused child rapist: "She's seen on two separate occasions, laughing at the girl who was raped. Kathy Shelton, that young woman, is here with us tonight."
THE FACTS: At no point was Mrs Clinton seen laughing at the victim.
In 1975, at the age of 12, Ms Shelton was sexually assaulted in north-west Arkansas. Mrs Clinton was asked by a judge overseeing the case to represent her alleged attacker. After the prosecution lost key evidence, Mrs Clinton's client entered a plea to a lesser charge.
In an interview a decade later, Mrs Clinton expressed horror at the crime, but was recorded on tape laughing about procedural details of the case. The audio has been seized on by conservative groups looking to attack her presidential candidacy but does not convey mirth at the girl's fate.
DONALD TRUMP on Bill Clinton: "He lost his licence. He had to pay an 850,000-dollar fine."
THE FACTS: Mr Trump's facts are, at best, jumbled. In 1998, lawyers for Bill Clinton settled with former Arkansas state employee Paula Jones for 850,000 dollars in her four-year lawsuit alleging sexual harassment. It was not a fine and there was no finding or admission of wrongdoing.
Mr Trump erred in describing the legal consequences of that case. In a related case before the Arkansas State Supreme Court, Mr Clinton was fined 25,000 dollars and his Arkansas law licence was suspended for five years. Mr Clinton also faced disbarment before the US Supreme Court but opted to resign from the court's practice instead of facing any penalties.
HILLARY CLINTON, in response to a question about her saying that politicians need to have "both a public and a private position" in a 2013 paid speech, said: "As I recall, that was something I said about Abraham Lincoln after having seen the wonderful Steven Spielberg movie called Lincoln. It was a master class watching President Lincoln get the Congress to approve the 13th Amendment."
DONALD TRUMP replied: "She lied. Now she's blaming the lie on the late, great Abraham Lincoln."
THE FACTS: Mrs Clinton's recollection is correct.
She invoked the movie Lincoln and the deal-making that went into passage of the 13th Amendment, which outlawed slavery, in an April 2013 speech to the National Multifamily Housing Council.
According to excerpts of the speech included in hacked emails published last week by WikiLeaks, Mrs Clinton said politicians must balance "both a public and a private position" while making deals, a process she said was like making sausage.
"It is unsavoury, and it always has been that way, but we usually end up where we need to be," she said according to the excerpts.
"But if everybody's watching, you know, all of the back-room discussions and the deals, you know, then people get a little nervous to say the least. So, you need both a public and a private position."
DONALD TRUMP, asked whether the predatory behaviour with women that he described in a 2005 video amounted to sexual assault, said: "No, I didn't say that at all."
THE FACTS: He certainly didn't own up to sexual assault in his boastful remarks in 2005. But he clearly described groping and kissing women without their permission, using his celebrity status to impose himself on them.
"I don't even wait," he bragged in the video. "And when you're a star, they let you do it. You can do anything."
He described a specific sexual advance toward a married woman, saying: "I moved on her like a bitch. But I couldn't get there."
No court has considered whether that is sexual assault, but some of the Republicans who abandoned support for his candidacy, as well as Democrats and activists, say it sounds like that to them.
HILLARY CLINTON: "I do think ... the use of (US and coalition) enablers and trainers in Iraq, which has had some positive effect, are very much in our interest."
THE FACTS: She is right about the positive effect, at least on the Iraqi military. After losing the city of Ramadi to the Islamic State group again in May 2015, the hundreds of US military trainers and advisers have made some gains.
It took more than a year, but the programme Mrs Clinton cited has produced a more competent Iraqi military and set the stage for an Iraqi campaign to retake the northern city of Mosul. That city has been the Islamic State militants' main stronghold since it swept into Iraq in 2014, almost unopposed by the Iraqi army.
As Mrs Clinton's characterisation of the programme suggests, it has not been an unqualified success and is expected to require years of additional effort to ensure that the Iraqi military does not collapse as it did in 2014.
HILLARY CLINTON: "After a year-long investigation, there is no evidence that anyone hacked the server I was using, and there is no evidence that anyone can point to, at all ... that any classified material ended up in the wrong hands."
THE FACTS: Maybe, maybe not. While there's indeed no direct, explicit evidence that classified information was leaked or that her server was breached, it was nevertheless connected to the internet in ways that made it more vulnerable to hackers - and the public may never know who saw them.
FBI director James Comey has said: "We assess it is possible that hostile actors gained access to Secretary Clinton's personal email account."
The Associated Press previously discovered that her private server, which has been a major campaign issue for Mrs Clinton and the focus of US investigations, appeared to allow users to connect to it openly over the internet and control it remotely. That practice, experts said, was not intended to be used without additional protective measures, and was the subject of US government warnings at the time over attacks from even amateur hackers.
Since AP traced her server in early 2013 to her home in Chappaqua, New York, Mrs Clinton has not fully explained who administered her server, if it received software updates to plug security holes or if it was monitored for unauthorised access. It is also unclear what, if any, encryption software her server may have used to communicate with official US government email accounts.
Comey has said Clinton and her staff "were extremely careless in their handling of very sensitive, highly classified information." But he said the FBI won't recommend criminal charges against Clinton for use of the server while she was secretary of state and closed the investigation.
DONALD TRUMP: "She (Mrs Clinton) wants to go to a single-payer plan, which would be a disaster ... she wants to go to single-payer, which means the government basically rules everything."
THE FACTS: It is Vermont senator Bernie Sanders - not Mrs Clinton - who supports a Canada-style government-run health care system.
While Mrs Clinton's proposals would expand the government's role in the health care system, she is not talking about dismantling the current system, which is a hybrid of employer-sponsored coverage, government programmes like Medicare and Medicaid, and individually-purchased insurance.
As president, Mrs Clinton would push for a government-sponsored insurance plan in the health care markets created by President Barack Obama's health care law, as an alternative to private insurance. But those markets currently cover about 11 million people, while about 155 million have job-based coverage.
In excerpts from Mrs Clinton's paid speeches she gave behind closed doors, though, she did praise Canada's universal coverage and said that single-payer systems were "as good or better" when it came to basic medical care. But she also noted drawbacks of such health care systems, such as longer wait times for procedures.
DONALD TRUMP: "I would not have had our troops in Iraq."
THE FACTS: He actually offered lukewarm support for invading Iraq before the war began. He has repeatedly and erroneously claimed to have come out against the war before it started, telling Howard Stern in September 2002: "Yeah I guess so," when asked if he would back an invasion.
This time, his claim was slightly different - that if he had been president at the time, he would not have invaded. It is conceivable, at least, that he would have taken a position in office at odds with his stance as a private citizen. A few months before the March 2003 invasion, he did tell Fox News that the economy and threats from North Korea posed greater problems than Iraq.
DONALD TRUMP: "I don't like Assad at all. But Assad is killing Isis. Russia is killing Isis."
THE FACTS: Not true. Syria's President Bashar Assad considers the Islamic State group to be among numerous "terrorist" groups that threaten his government, but his military is not fighting them. It is focused on combating Syrian opposition groups, some of which are supported by the United States.
The fight against the Islamic State militants is being waged by a US-led coalition, with help from Turkey, by training, advising and equipping Syrian Arab and Kurdish fighters. While Moscow asserts that it is fighting the Islamic State extremists in Syria, the vast majority of its air strikes has targeted opposition groups threatening the Assad government.
DONALD TRUMP: "She is raising your taxes and I am lowering your taxes. She's raising everybody's taxes massively."
HILLARY CLINTON: "He would end up raising taxes on middle-class families"
THE FACTS: Mrs Clinton is not raising taxes on "everybody". Nearly all of her proposed tax increases would affect the wealthiest 5% of Americans, according to the non-partisan Tax Policy Centre.
Mr Trump is proposing massive tax cuts for both individuals and businesses. Yet it is not clear that all Americans would benefit. The conservative Tax Foundation estimates that the bottom 80% of taxpayers would see their after-tax income rise from 0.8 to 1.9%. The wealthiest 1% would see their after-tax incomes rise at least 10.2% to 16%.
Yet Mrs Clinton may be right that Mr Trump's proposals would increase taxes on many middle and lower-income families. Mr Trump's plan eliminates the personal exemption, which currently allows households to reduce their taxable income by 4,050 dollars for each member of the household, including children. He would replace that with higher deductions, but for many single parents and families with three or more children, the standard deduction wouldn't be large enough to offset the loss of personal exemptions.
HILLARY CLINTON: "If we repeal (Barack Obama's health care law) as Donald has proposed, all of those benefits I have mentioned are lost to everybody ... and then we will have to start all over again."
THE FACTS: Mrs Clinton is essentially correct. Congressional Republicans have promised their replacement plan for Mr Obama's health care law would provide coverage for the uninsured, but they have not provided enough detail to allow a rigorous comparison. A complete repeal of the health care law would wipe the slate clean and politicians would have to start over.
Republicans have expressed support for some goals of the health care law, such as assuring that people with health problems can get coverage, but whether a Republican replacement plan would work as well remains to be seen. Mr Trump's own plan was recently evaluated by the Commonwealth Fund and the RAND Corporation, and the analysis found would increase the number of uninsured people by about 20 million.