What was going on when I was born?

The State of Delaware, in a break with normal practice in the municipal bond market, announced Friday that it wants to sell $50 million of tax-exempt bonds using a system in which records of bond ownership are kept electronically, with no paper certificates available to investors. The paperless book-entry system is widely used for Treasury and United States agency securities, but is little- known in the municipal bond market. If investors accept the innovation, it could significantly reduce expenses for local governments and securities dealers. ''The book-entry system is the wave of the future,'' said Janet C. Rzewnicki, the Treasurer of Delaware. ''If it is accepted, we could end up with lower costs associated with our borrowings, in terms of printing, the signature company, the transfer agent, the registrar and the paying agent.''

The Economy The Federal Reserve appears willing to give up some of its powers over commercial banks as part of a plan to create a new Federal Banking Agency, according to an Administration official. The Fed's stance could break a longstanding deadlock over what its regulatory role should become. (Page D1.)

Excerpts from the debate, page B8. HANOVER, N.H., Jan. 15 - The eight major Democratic Presidential candidates engaged in the sharpest exchanges of the new campaign year today in a nationally televised debate that produced a shouted confrontation between Walter F. Mondale and Senator John Glenn. The exchange between Mr. Glenn, an Ohio Democrat, and Mr. Mondale, the former Vice President, centered on the cost of programs favored by Mr. Mondale and on his call for legislation to protect the American automobile industry from foreign competition. At one point, Mr. Mondale leaped to his feet, shouting ''Who has the floor here?'' and condemned Mr. Glenn's figures as ''baloney.'' Another rival, the Rev. Jesse Jackson, stepped in to chide the two, saying their discussion should be ''in a serious vein.'' Senator Gary Hart of Colorado also jumped in, telling the two obviously angry candidates, ''Quarreling between the two of you as to whose mistakes were the worst is not going to win the election or govern this country.''

As late as the mid-1970's, the world of photofinishing seemed to belong to the Fotomat Corporation. Its blue and gold kiosks multiplied in shopping malls and parking lots across America at the rate of 500 a year. Its revenues and earnings tripled in the space of five years. Some people called it the McDonald's of photography. But Fotomat's fortunes have turned blacker than a roll of overexposed film, and in the last two years the company has watched its kiosk empire deteriorate. ''I gave up on them years ago,'' says Brenda Lee Landry, an analyst at Morgan Stanley & Company.

One year ago Apple Computer Inc. hoped to dazzle the computer world with a revolutionary new machine called Lisa that was said to be the key to the company's future. But Lisa turned out to be a poor seller, and Apple's earnings and its leadership in the personal computer market crumpled under an attack from the International Business Machines Corporation. Now Apple is preparing to try again with another new machine called Macintosh, which will be introduced at the company's annual meeting on Jan. 24. The stakes for Apple are even higher now, especially if it wants to remain a force in the computer business. It is Apple's third and probably last chance to reduce its dependence on its Apple II line, which is nearly seven years old. Macintosh, which is expected to sell for $2,500, is only part of Apple's strategy. The company is also announcing newer, faster versions of its Lisa with an entry price as low as $3,500. And later in the year the company is expected to announce two new versions of its Apple IIe and to push that product more strongly into the home market.

A picture that appeared Wednesday with articles about diplomatic relations between the United States and the Vatican was incorrect. It showed Rufus King, a member of the Continental Congress and later a United States Senator, not the Rufus King who was Minister to the Papal States under Pope Pius IX.

An article Jan. 6 on acquired immune deficiency, or AIDS, referred ambiguously to a group at risk of contracting the disease. It should have stated that people born in Haiti but living in the United States now account for 5 percent of the total number of disease victims in the United States.

Within one of New York City's more obscure but passionate subcultures, that of the railroad aficionado, the name Peter Obletz ranks with that of, say, Ferdinand Magellan. In this circle, Mr. Obletz's esteem as an explorer is undiminished by the less-than-exotic location of his discovery, an abandoned railroad line near Manhattan's western shore - a discovery he has set out to preserve. Four years ago, Mr. Obletz, now a consultant on subway advertising for the Metropolitan Transportation Authority, lived in two elegantly appointed dining cars on space he rented on 30th Street in the old Penn Central yards along the Hudson River. The siding sat in the shadow of a long, overhead structure between 10th and 11th Avenues that piqued Mr. Obletz's curiosity enough for him to investigate. He found an outdoor metal staircase 17 feet high, climbed it, and walked onto what he said looked like a broad, ramshackle highway cutting through the Chelsea section and into Greenwich Village. For two miles, from 34th Street to Washington Street, he ambled in silence unusual for Manhattan - over weeds, over garbage, and, more important to him, over railroad tracks.

In the world of smuggling these days, fashion is the fashion. Recent trophies among customs inspectors include 100,000 counterfeit Lacoste alligator emblems, 759 cartons of fake Jordache jeans and $17 million worth of Taiwanese shorts- and-shirt sets slipping into the country under quotas for swimwear. ''These are multimillion-dollar shipments,'' Edward Kellmer, a United States Customs agent, said. ''It's better than smuggling diamonds.''

Telerate Inc., the dominant provider of electronic financial information in the United States, has 350 sources in the banking and securities community feeding it information on trades as they occur, which may involve as many as 500,000 price updates a day. It has 8,000 viewing terminals on the desktops of financial institutions in the United States, including all 100 of the country's largest banks and 46 of the 50 biggest securities companies. But Reuters, its chief rival and a company with enormous strength in Europe, may be on the verge of mounting a strong challenge to Telerate on its home turf. Reuters, which also operates an international news service, is expected to reap about $1.4 billion from its plan to go public this spring. The influx of money, plus the possibility of attracting a major new source of credit market information, could put Reuters in a position to increase its American presence dramatically, analysts believe.

The Government of Gen. Gregorio Alvarez, faced with growing public discontent after more than 10 years of military rule, has reimposed a crackdown on political dissent. The crackdown and other developments could cause a postponement of elections scheduled later this year, according to disenchanted Government officials, opposition leaders and Western diplomats. The unrest comes as Argentina, Uruguay's powerful neighbor, which has had much influence in this country, ends nearly eight years of military rule to return to democracy under the newly elected President Raul Alfonsin. The Argentine example has been stimulating the demands by opposition leaders and ordinary Uruguayans for democracy here too. In addition to the crackdown, General Alvarez, a 58-year-old retired general who was elected in 1981 by the ruling junta of 26 generals and admirals to lead the transition to democratic rule, is maneuvering to stay in power, the senior Government officials and Western diplomats say. General Alvarez had apparently been losing the support of the junta members, they said, but he has been regaining backing as the new Argentine Government has begun prosecuting former military leaders for their abuses of power. Uruguay's military Government, which had been loosening its rule, has promised it will hold elections in November and step down in March of 1985. The Government officially affirms that the election will be held as scheduled, but two weeks ago a senior official cast doubt on that promise for the first time in public.

John McEnroe put on a tennis clinic at Ivan Lendl's expense yesterday, reversing the outcome of last year's Volvo Masters final with a commanding 6-3, 6-4, 6-4 victory. McEnroe was in control of every aspect of his game - and of his temper - but nowhere was his mastery more obvious than in his serve and reflex volley. He succeeded with 63 percent of his first serves, keeping Lendl off balance with varied placement. His volleys were so deep and his touch so sure that Lendl was unable to lob and at times looked helpless to defend against the bullets aimed at his feet and body.