AMERICANS like criticizing their government. On any given day in any large U.S. city, elected officials field a bewildering array of complaints, ranging from relatively trivial matters of garbage pickup and snow removal to deeper issues of police brutality and development.

And most officials believe they have a responsibility to respond to these problems, whether great or small.

"You the Mayor?" The Education of a City Politican

By Barabara Ackermann

Dover, Mass: Auburn House Publishing Co.

$24.95

But solving them can be difficult. City bureaucracy often has a life of its own, with each city agency performing its own particular function in its own particular way. An outsider trying to get anything done in a city government must clear a path through an administrative jungle simply to understand what is going on.

"You the Mayor?" is written from this outsider's perspective. While 10 years on the Cambridge City Council--including two as mayor--should qualify Barbara Ackermann as an expert in the quirks of city government, one gets the sense that she never really feels confident about her abilities. Rules of politics and government that are second nature to a native like Councillor Alfred E. Vellucci, now the mayor, are an unfolding mystery to a relative newcomer like Ackermann.

And Ackermann's perspective is exactly what makes "You the Mayor?" an informative book--not only about Cambridge but city politics in general.

Ackermann does not lecture. She describes the the things she learned while trying to solve some of her constituents' problems.

SOME lessons come easily. In the early chapter "Nine Ayes," Ackermann describes her discovery that much of the council's business is simply a matter of form--her fellow councillors approve virtually any order she brings them, as long as it does not involve money. Attempts to deal with the semiautonomous Redevelopment Authority teach her the three I's that often dominate city administration--inertia, indolence and incompetence.

But most of the problems with which Ackermann tries to deal are too complex to be neat little dictums. One of the book's major themes is the escalation of violence in the city during the 1970s, beginning with the takeover of University Hall in April, 1969.

Ackermann sees the so-called "Peace Wars" as a tragic example of violence begetting violence. Police who were not trained to handle peaceful demonstrations let events get out of control and did not know how to respond.

While Ackermann was mayor in 1972, a 16-year-old high-school dropout named Larry Largey was found dead in a police cell. A police autopsy claimed he died of a drug overdose. City activists claimed he was beaten to death by the police.

News of Largey's death touched off a wave of riots in Roosevelt Towers, the East Cambridge housing project where he lived, as angry youths protested what they believed to be a murder of one of their own.