The Dow Jones industrial average surged nearly 670 points, erasing nearly half the ground it lost last week and marking the biggest gain since August 2015.
The broad gains Monday were led by technology stocks and banks, which took some of the biggest losses last week as trade tensions flared between the U.S. and China.
Investors were encouraged by signs Washington and Beijing are open to negotiating on trade.
Microsoft jumped 7.6 percent and Bank of America climbed 4.4 percent.
The Dow rose 669 points, or 2.8 percent, to 24,202.
The S&P 500 climbed 70 points, or 2.7 percent, to 2,658. The Nasdaq climbed 227 points, or 3.3 percent, to 7,220.
Bond prices fell. The yield on the 10-year Treasury note rose to 2.84 percent.