HEMPSTEAD, N.Y. — Donald Trump repeatedly clashed with Hillary Clinton during Monday’s first presidential debate, interrupting her and appearing agitated at times as they tangled over the economy, her use of a private mail server and his unwillingness to release his income tax returns. Clinton maintained an even demeanor, smiling indulgently when Trump turned aggressive.

Clinton and Trump engaged in a vigorous back-and-forth on the debate stage at Hofstra University as polls showed them locked in a tight race. Given the wide interest in Trump, the business mogul and former reality TV star, and Clinton, the first woman to win the nomination of a major party, the debate was expected to draw a massive viewing audience.

Here are the top takeaways from Monday’s debate:

TRUMP’S TEMPERAMENT

If Clinton aimed to get under Trump’s skin in the first 30 minutes of the debate, the Democratic nominee appeared to succeed. Clinton often put Trump on the defensive, saying he had “rooted for” the collapse of the housing industry and had considered climate change to be a hoax. In another exchange, Clinton said, “I have a feeling that by the end of this evening I’ll be blamed for everything that ever happened.”

Trump interjected, “Why not?” Later on, Trump said he had a “winning temperament,” prompting Clinton to respond: “Whew. OK.”

CLINTON’S ZINGERS

Often delivered with a smile, Clinton came prepared with pithy lines that undercut Trump’s case on the economy. In an early exchange, Clinton said Trump would push for “trickle-down” tax cuts that would only benefit the wealthy, calling it, “trumped-up trickle-down.” When Trump got in a dig at Clinton’s absence from the campaign trail, she said there was nothing wrong with spending time preparing for the debate. “You know what else I did?” she asked. “I prepared to be president.”

THE OUTSIDER

Trump repeatedly underscored his role as a political outsider, questioning the economic stewardship of President Barack Obama and the administration of former President Bill Clinton, who sat in the front row. Describing the loss of manufacturing jobs in states like Michigan and Ohio, Trump said Clinton had been in government for 30 years, asking, “Why are you just thinking about these solutions right now?”

TRUMP’S TAXES

Clinton savaged Trump with a lengthy explanation of why Trump won’t release his tax returns, concluding he’s got something to hide. She said Trump may not be “as rich as he says he is” or “maybe he’s not as charitable” as he says he is. Clinton warned that perhaps Trump hadn’t paid any federal income tax at all, noting that some of Trump’s income tax returns in the 1970s showed he had paid no federal income taxes in certain years.

CLINTON’S EMAILS

Clinton gave arguably her most concise answer to questions about her use of a private e-mail server as secretary of state, taking responsibility and giving Trump nowhere to go. Despite her past statements in which she changed her story from previous iterations or left wiggle room by not being completely accurate, on Monday she avoided getting wrapped up in a lengthy exchange over one of her biggest liabilities. When Trump said he would release his tax returns if Clinton put out what he called her “33,000 deleted” e-mails, Clinton said, “I made a mistake using a private e-mail” server. Trump interjected, “That’s for sure,” prompting Clinton to respond, “I take responsibility for that.”

GENDER WARS

Clinton turned the tables on Trump when he was asked to respond to his assertions that she doesn’t have the “stamina” to be president. Trump questioned whether Clinton has the physical fitness to be president and he repeated the criticism directly to her. Clinton replied that Trump shouldn’t talk about stamina until he’s tried to maintain a busy schedule like she kept up as secretary of state. And then she dug into him, adding, “This is a man who has called women pigs, slobs and dogs.”