At the close of trading, the Nasdaq composite index gained 76.22 to 1,499.41, and the Dow Jones industrial average rose 368.05 to 8,603.86.
Last week, both indexes suffered major losses. The Nasdaq lost 16.1 percent and the Dow dropped 14.3 percent.
Now that stock prices have come down significantly, analysts are saying it is time for some bargain hunting. Even Barron's, a publication hardly known for its cheerleading, said last week's sell-off was likely to be a good opportunity for investors. The big question is how long stocks will move higher.
Goldman Sachs strategist Abby Joseph Cohen, traditionally a bullish analyst, urged investors to add more stocks to their portfolios. Cohen said she has upped her recommended stock weighting to 75 percent from 70 percent. She added that equities are likely to do better than bonds because of five main factors: cheap stock prices, government action to boost the economy, share repurchases, a wealth of cash reserves, and confidence from the markets' ability to reopen smoothly last week.
"Things really got out of hand last week," said Mark Coffelt, manager of the Texas Capital Value & Growth Portfolio. "It was the worst week since the Depression, but we're not even close to that. In fact, we're pretty close to an economic upturn. We've already seen the worst in stocks and in the economy."
Among stocks in the news, Internet security and domain name registrar VeriSign, up $1.56 to $39.86, said Monday that it will buy Illuminet Holdings in a $1.2 billion stock swap. Illuminet rose $1.39 to $36.37.
JDS Uniphase, up $1.03, or 19 percent, to $6.39, said sales will come in slightly below estimates for the current quarter, but added that business appears to be stabilizing. The maker of fiber-optic equipment said its first-quarter sales are expected to be around $325 million.
Top-gaining sectors included storage; EMC rose $1.70, or 15 percent, to $12.85, and CNET's storage index gained a whopping 10 percent.
Enterprise stocks were also strong, with CNET's server hardware index up 6 percent, led by Sun Microsystems, which jumped 77 cents, or 10 percent, to $8.73. CNET's server software index was up around 10 percent.
Among the most actively traded gainers, Intel rose $1.95, or 10 percent, to $21.25; Oracle rose $1.76, or 16 percent, to $12.52; Cisco Systems was up 47 cents to $12.56; and Microsoft rose $2.30 to $12.56.
AOL Time Warner gained $2.65, or 9 percent, to $32.50, and Yahoo rose 57 cents, or 7 percent, to $ 32.50.
Staff and Reuters contributed to this report.