By German Lopez

• Trump declared that “America’s decline is over” and that “the golden age of America begins right now.” He said a “radical and corrupt establishment has extracted power and wealth from our citizens, while the pillars of our society lay broken and seemingly in complete disrepair.” He vowed to fix the country.
• He promised swift action on the economy, immigration, national security and social issues. He said he would invoke an archaic federal law, the Alien Enemies Act of 1798, to eliminate “foreign gangs and criminal networks.”
• Trump repeated a pledge to rename the Gulf of Mexico as the Gulf of America, eliciting a laugh from Hillary Clinton. And he said he would restore William McKinley’s name to the country’s tallest mountain. (The Obama administration renamed it Denali, which is what Alaska’s Native population calls it.)
• He said it was now government policy that there “are only two genders: male and female.”
• His tone was aggressive, a warning to domestic and foreign audiences that America under a more experienced Trump will not take no for an answer, David Sanger writes.
• Trump made false claims about the Panama Canal and the 2020 election. Here’s a fact-check of the speech.

• Because of below-freezing temperatures in Washington, Trump’s inauguration took place inside the Capitol Rotunda. The podcaster Joe Rogan sat onstage, as did several tech executives including Jeff Bezos, Mark Zuckerberg and Tim Cook. This graphic shows who was among Trump’s inner circle.
• “For the many billionaires who bought their way in, it was both a flex and act of public deference to be there,” Shawn McCreesh wrote. Read about the awkwardness onstage.
• Many guests — including Ron DeSantis and the YouTuber Logan Paul — had to sit in an overflow room and watch the ceremony on a screen.

• Melania Trump wore a black hat with a wide brim. “Whatever she was thinking was impossible to see — by design,” our fashion critic, Vanessa Friedman, wrote.
• The country singer Carrie Underwood performed an a cappella rendition of “America the Beautiful,” summoning the crowd to join her after the background music failed to play. Watch the video.
• See photos of the day’s events.

• Immigration. Trump declared a national emergency over the U.S.-Mexico border, which unlocks federal funds to build the border wall and turn back more migrants. He also put restrictions on asylum and made border security a military priority. And he moved to end birthright citizenship, a right that the Constitution guarantees.
• Tariffs and trade. Trump directed federal agencies to investigate potentially unfair trade practices. He also called for an assessment of previous trade deals, particularly those with China, Mexico and Canada. And he moved to create a new agency, the External Revenue Service, to collect tariffs. Trump has not yet imposed new tariffs.
• Energy and the environment. Trump withdrew the United States from the Paris Agreement, an international climate pact. He declared a national energy emergency and eased regulations to allow more domestic oil and gas production.
• TikTok. Trump stalled enforcement of a ban on TikTok for at least 75 days, giving ByteDance, the app’s Chinese owner, more time to find a way to stay in the country. In the meantime, TikTok will stay online.
• Other issues. Trump ended remote work for federal employees and froze most federal hiring. And he withdrew the United States from the World Health Organization.

• Trump granted clemency to all the nearly 1,600 people charged over the attack on the Capitol on Jan. 6, 2021.
• He pardoned Enrique Tarrio, the former Proud Boys leader, and he commuted the sentence of Stewart Rhodes, the founder of the Oath Keepers militia.
• “An unspeakably joyous, happy day”: Dozens of people celebrated the pardons outside a jail in Washington.
• With the stroke of a pen, Trump erased the biggest and most complex investigation in Justice Department history, Glenn Thrush wrote.

• Hours before the end of his term, Joe Biden issued protective pardons for several people the Trump administration might prosecute. The list included Anthony Fauci, House members who investigated the Jan. 6 Capitol riot, and members of the Biden family.
• JD Vance, 40, took his oath as the youngest U.S. vice president in over 70 years.
• Trump has brought back his reality-show spectacle, our TV critic wrote.
• Trump’s supporters filled Washington’s streets with a sense of triumph and gloating.
• Vivek Ramaswamy quit as co-leader of what Trump has labeled the Department of Government Efficiency. He plans to run for governor of Ohio, and he also had tensions with Elon Musk.
• Jon Stewart and the other late night hosts discussed the inauguration.

• The cease-fire let Gazans return to their homes. Many are sifting through wreckage.
• Many Israelis feel conflicted about the cease-fire deal: More than 30 hostages will likely be freed, but Hamas could now remain in power in Gaza.
• Israel’s defense minister told the military to prevent mass celebrations in the West Bank as Palestinian prisoners are released.
• A senior Hamas official said the group was open to improving its relationship with the U.S.

• Southern California is braced for powerful winds. Officials say they are now better prepared for extreme fire danger.

• The lead content of Los Angeles’ air reached 100 times its normal level as the fires consumed old pipes and paint.
• One Altadena couple found help from a local expert to save their pets of 25 years: five koi fish.

• In Colombia, clashes between two rival armed groups have killed at least 80 people and forced thousands to flee.
• An Indian court gave a life sentence to a man convicted of raping and murdering a trainee doctor in Kolkata. Her killing inspired national outrage.
• A winter storm in the southeastern U.S. brought sleet and snow to the Gulf Coast.