CITIZEN JANE: The True Story of Jane Fonda, by Christopher Anderson (Virgin Books, $102). SHE is a fine actress, a shrewd businesswoman, a fitness guru and a political activist, but above all else, Jane Fonda is majestically annoying. In Citizen Jane, Christopher Anderson documents the chameleon-like changes in Fonda's personality, from her sci-fi sex kitten Barbarella days to her new life as media mogul Ted Turner's wife. Even her most ardent detractors must concede that she deserves admiration. Surprisingly, her life story is more compelling than it would first appear, not simply because she grew up among some of the greatest Hollywood stars, but because of her insatiable desire to make a contribution to a society she never had a remote chance of understanding. Fonda is the typical limousine liberal - a communist who eats caviar, a woman's libber who was never oppressed, a fitness guru with bulimia - but she managed to march as a leader for the communists in Vietnam, the woman's rights movement and the fitness craze, and do a fair bit of good along the way. Born on December 21, 1937, to Henry Fonda and Frances Seymour, she grew up in the halcyon days of Hollywood, bouncing on the knees of Jimmy Stewart and John Wayne but rarely on those of her father or mother. Anderson uses this theme of parental neglect as one of the key motivating factors in Fonda's life, pushing her to rebel at private school and later to pursue her acting career with a vengeance, but with his apparently small reservoir of talent to draw from, the author is unable to make the reader sympathise with Fonda. Calling Henry ''daddy'' and using Jane's childhood nickname Lady to recreate life in the Fonda household, Anderson's portrayal reveals a cast of superficial megalomaniacs who never reveal their humanity despite suffering tragedy which automatically touches the reader. When Jane's mother committed suicide, Henry Fonda chose to act in a play that night, while his daughter was unable to cry. By the age of 10, according to Anderson, she had ''learned that she could depend on only one person - herself''. Ironically, ''independent'' Fonda has gone through her life seeking men she could depend on, substitutes for the father figure she never really had. In the swinging '60s she went to Paris and ended up marrying the plain-looking but legendary sexual rake Roger Vadim, who had also married Brigitte Bardot and had a child with Catherine Deneuve. It was Vadim who introduced Fonda to the hip New Left crowd in Paris, but he was more interested in turning her into a sex symbol than a political protester. After proving her skills in such films as Cat Ballou and Barefoot in the Park, Fonda decided her life with Vadim was over and, intrigued with the political turmoil in the US, she decided it was time to become a woman of the people. It is this section of Anderson's book which is the most interesting, if only because the author resists the temptation to side with his subject on every issue. Rather than writing a Fonda apotheosis, Anderson chronicles her blunders, her misuse of facts, her superficial understanding of politics and how she alienated the people she wanted to help. Her reputation as a political dilettante flying on the wings of her radical left new husband, Tom Haydon, is justified by the facts, and even ''Hanoi Jane'' admits making serious political and factual errors. But throughout this embarrassment, Fonda managed to win two Oscars and produce Oscar award-winning films like The China Syndrome, proving real talent lay firmly embedded beneath the thin political guises she so frequently donned. Anderson is a journeyman writer, incapable of departing from his department-store psychology in order to draw any profound conclusions, but his honest, straightforward portrayal is worth something in an age of scandal-seeking, opportunistic exposes. In his conclusion, Anderson says Fonda will continue to ''amaze us'' and, as her new-found role as the happy housewife is a far cry from the outspoken feminist she was in the '70s, there is little doubt a new Fonda incarnation is already in the works. Dislike her as you might, at least she is an original.