Marion Shepilovk Barry Jr., who as a child chopped cotton by his mother's side in the fields of Arkansas and who came to Washington 14 years ago as a militant black community activist, was sworn in yesterday as the second mayor of the District of Columbia since 1871.

Calling Washington "a city filled with contradictions and contrasts" in which "our greatest hopes lie side by side with helplessness and despair," Barry pledged to unite District of Columbia residents in "a full governing parthership" to make Washington a "great city."

"If we value cooperation over conflict, neighborhood stability over chaos and disruption, compassion over complacency, economic justice over profit and human decency over the destruction of humanity," the one-time social reformer said in his inaugural address, "we can accoumplish what others have only promised and forgotten."

Earlier, at an inaugural breakfast, Barry said, "Let there be no mistake about it that here in Washington, D.C., we will be our brother's keeper."

Barry's inaugural speech, delivered shortly after he took the oath of office at 12:44 p.m. from U.S. Supreme Court Justice Thurgood Marshall, laid out a broad action agenda for his four years in office.

He pledged to improve schools and housing in the city, provide more jobs for youth and decrease the city's unusually high infant mortality rate. His will be an "open, compassionate and responsive city government," Barry said.

The theme underlying much of yesterday's often muted excitement was change. New and younger men -- Barry, 42, and the new City Council Chairman Arrington Dixon, 36 -- were coming to power. It was, said the Rev. Henry C. Gregory during the morning breakfast, a passing of "the torches to a rising generation."

The heavy, wind-blown rains that dampened the nation's capital apparently doused some enthusiasm. But it did not stop scores of persons from crowding in the hallway outside the overflowing City Council chambers on the fifth floor of the District Building to hear the swearing in ceremonies.

Members of high school bands and drill teams, who at one point had huddled in the doorways of dry cleaners and liquor stores to escape the rain while waiting for the parade to begin, found extra enthusiasm to step with when they passed Barry and his wife, Effi, in front of the District Building.

'Go on and do it," the mayor shouted at one group, tapping his foot while Effi Barry, standing beneath an umbrella, waved a small miniature District of Columbia flag back and forth in time to the music and bounced up and down.

The day was the personal culmination of years of struggle for Barry, a Democrat who had steadily climbed the local political ladder in well-calculated steps -- from community activist to school board president, to atlarge city councilman and finally to underdog victor in the race for mayor.

"My Lord, what a morning," Barry exclaimed quoting an old Negro spiritual as he looked out on the 2,000 persons who had come to breakfast.

The weather did have Reb. Jesse L. Jackson, who was supposed to be the breakfast guest speaker was snowbound in Chicago. Only a fraction of the marching units expected to take part in the parade did so, and there were only small clusters of people along the parade route.

Because of the rain, inaugural day activities were so dealyed that Vice President Mondale, who had a tight schedule was unable to appear at a reception at the District Building.

And the rain and street closings for the parade caused large traffic jams for many commuters.

"I guess Barry's entitled to tear up the city as well as anybody else," said one person, philosophically, hurrying across 13th Street.

Still, Barry marching much of the parade route arm in arm with his wife, Effi, was in high spirits, as were many of those who came over to greet him. And the day was marked with several moments of very personal joy, sentiment and humor:

Barry's deeply religious mother, Mattie Cummings, up from Memphis for the inauguration, hung her head, shook it from side to side and chocked back tears as the Rev. Leamon White gave the opening prayer for the inauguration of her only son as mayor of the nation's capital.

For a moment, as he walked down U Street past the 16th Street headquartrs of Pride Inc., the self-help organization that Barry cofounded and used as a srpingboard to political prominence, the new mayor was at a loss for words. "I'm proud of you boy, God, I'm proud of you," a fellow one-time activist said, rushing into the street to pump Barry's hand. "We came a long way.We gonna turn it around."

During swearing in ceremonies at the District Building, former Mayor Walter E. Washington, replaced by Barry after 11 years in office, jokingly admonished a slow-moving bystander who was delaying Washington's ceremonial presentation of the city seal to Barry. "Sit down," Washington said. "This is one of my lat acts."

Barry, who clinched the mayor's race in a closely fought three-way Democratic primary by a margin of fewer than 2,000 votes, sounded a theme of unity throughout the day, blended with promise for a new enthusiasm in the city to accomplish unprecedented goals.

"Let this day mark the beginning of a new and unfied Washington community," he told 2,000 persons at a $10-a-plate inagural breakfast. "Let this day signal our drive toward greatness"

Rep. Ronald V. Dellums (D-Calif.), who replaced the snowbound Jesse L. Jackson as guest speaker at the breakfast, called Barry's taking of power a moment of "high expectation and great hope."

Dellums, who is expected to become the new chairman of the House District Committee, said the District should be a showcase of federal efforts to save the cities. He said the nation's capital, under Barry's leadership, offered a "significant alternative" to increasing political conservatism in America, including, he said, the political tone at the White Houe.

For a while, it appeared as if the heavy rains would cancel plans for the parade. But inaugural chairman Thornell Page, observing several dozen bandsmen from McKinley Tech High School who had assembled for the parade said, "Look at all these kids out here. I can't cancel this parade. It's on."

Led by a wedge-like phalanx of 11 motorcycle policemen, the parade crawled down U Street, the usually well-traveled corridor whose cleared streets evoked eerie memories of the pall of city street life during the riots of 1968.

There and on 14th Street, which took the brunt of the 1968 rioting, there were still boarded up store-fronts now plastered with fragments of signs, vacant lots where buildings once stood and stark evidence of one of the city's newer problems -- real estate rehabilitation and the displacement it causes.

At some points, Barry marched past three-story Victorian house where, side by side, poor-looking residents waved from one window with towels over their heads as numbrellas and construction crews renovating houses stuck their hard-hat covered heads out of windows in the building next door.

Barry first began walking at 17th and U, a block from Price, and stopped to shake hands in the door-way of the large three-story building on the corner of 16th and U Streets.

"This street, this neighborhood, evokes such fond memories," Barry told a reporter. "It takes you back a number of years to when we were working, not knowing what it would lead to, not knowing what I would be doing. I's just sort of a euphoric feeling."

There were nevertheless some suggestions that Barry has still to win some full-fledged believers. "Okay." yelled one skeptical-looking women standing under an umbrella at 14th Street and Rhode Island Avenue. "Just let me see you do it, now."

The new City Council chairman, Arrington Dixon and his wife, Sharon, also walked much of the parade route, at times many yards behind Barry and without umbrellas. "I don't need one of those things," Dixon, his coat wide open and blowing in the wind, told a man who offered him an umbrella on 14th Street.

Then Dixon went back to greeting bystanders.

"Heappy New Year."

"Peace."

"Four big years," he said, smiling and holding up his fingers. "We ought to yell at Jimmy (Carter) while we're out here," he told Barry, as the parade passed two blaocks from the White House.

In his inaugural speech, Barry began many of his pledges with the words "as partners" -- to emphasize what he said would be an effort to work with citizens -- and a stand," his principal campaign slogan.

The candidate who had criticized Washington's government as one of "bumbling and bungling," said he would improve city services and "set the stage for a new emphasis on the arts." Barry said he would reduce crime, promote minority business and preserve the sanctity of "churches, synagogues, temples... and our families, which serve as the binding force of our society."

Barry closed by quoting the last words of "Lift Ev'ry Voice and Sing," generally regarded as the black national anthem.

"The time for talk is over. Our task is before us," he said. "Facing the rising sun of our new day begun, Let us march on till victory is won."

An inaugural party and disco was held last night and a business, professional and labor luncheon, designed to raise money to pay inaugural costs, is scheduled for today at the Washington Hilton Hotel.

There were strong echoes in the inaugural of the civil rights movement and Barry's own history as a Southern civil rights activist. James Foreman, the longtime leader of the Student Nonviolent Coordinating Committee, who sent Barry here to head the local SNCC office in 1965, gave Barry congratulatory hug in the mayor's new office.

After Justice Marshall, who was a noted civil rights lawyer, swore him in, the new mayor. told Marshall, "You characterize the great strength, commitment and compassion of the American ethos -- and you are a living symbol of the struggle for justice, equality and human dignity."

Some 300 persons in the council chambers rose to their feet and gave Marshall sustained applause.

Also sworn in yesterday wee six members of the City Council: David A. Clarke (D-Ward 1), Polly Shackleton (D-Ward 3), William R. Spaulding (D-Ward 5), Nadine P. Winter (D-Ward 6), Hilda Mason (S-At Large) and Betty Ann Kane (D-At Large). All but Kane were incumbents.

After taking office, Barry signed 18 executive orders, realigning the mayor's office staff and formally appointing some of the key aides whose selection he announced last week.

Barry appointed Elijah B. Rogers, city manager of Berkeley, Calif., as city administrator and Ivanhoe Donaldson. Barry's longtime friend and confidant, as general assistant to the mayor.

Four of Rogers's five assistant city administrators were appointed: Gladys W. Mack, Judith W. Rogers, Carroll B. Harvey and Colin F.S. Walters.

Barry also formally appointed Florence Tate as press secretary, Dwight S. Cropp as executive secretary to the mayor David Splitt as director of the office of documents and he reappointed George R. Harrod as personnel director.

Robers, whos was till in Berkeley, telephoned Barry during the signing ceremony and spoke to the new mayor over a speaker telephone. "I'm looking forward to joining the team," Rogers said.

"Well," Barry responded, "just get here."