REMIND ME WHO I AM, AGAIN. By Linda Grant. 301pp. Granta. Pounds 14.99. - 1 86207 171 3.

Remind Me Who I Am, Again is about senile dementia, which seems to have replaced anorexia as the most written-about disease. The day I started this review, the Guardian had a front-page story about the broadcaster Jon Snow. He was about to make a "high-profile speech to royalty and charity workers", it said, about the guilt he felt at putting his mother in a home because she had Alzheimer's. Linda Grant's book tells the same story. Her mother does not have Alzheimer's but MID (multi-infarct dementia) which has different causes but the same effect: memory loss.

Grant's book is an in-your-face, let-it-all-hang-out affair - brutal, repellent even, but free from any smarmy self-justification and immensely readable, if you can bear it. Her cliche-free prose manages to be both colloquial and elegantly economical; every detail tells, the dialogue is terrific, and the characters so vivid they could keep a novel going; while the intercutting of present and flashback is worthy of the Coen brothers. There is repetition, but repetition is part of Grant's theme, and when it occurs, it's startling rather than boring. She intertwines her mother's descent into madness with thoughts about memory and the way it governs our idea of who we are; and with her own family's history in the twentieth century. That history goes back no farther, because all her grandparents were Jewish immigrants from Eastern Europe. One of them was illiterate, and none had access to family graves or documents about their past, except for a few photographs, reproduced here in nostalgic sepia with all their creases and cracks. They had to reinvent themselves for their new environment, and so their history is as mythological as the Odyssey.

Grant draws parallels between being an immigrant and having dementia: "if your personal history is inaccessible, is it surprising that all you can engage in is the manufacture of myths?", she writes on page 48. By page 294, she has read and talked to psychologists and neurobiologists and learnt that it's like that not just for immigrants: "The self isn't a little person inside the brain, it's work-in-progress, 'a perpetually reconstructed neurobiological state, so continuously and consistently reconstructed that the owner never knows it's being remade.' Memory, then, is a fabrication, a re-interpretation, a new construction of the original."

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Grant's own odyssey began in Liverpool in 1951. Her rumbustious father had made it by manufacturing hairdressing equipment at the time of beehives and rollers (and was later ruined by Vidal Sassoon's geometric cut). Her lively, pretty mother came from an immigrant slum. On a photograph taken at the time, she "smirks", because she has "grabbed" a rich man. Grant never pretends to like her. She went in for huffs and grudges, and was not very interested in her two daughters. Later on, she complained about their going to university and never coming back to her. She would have preferred them to leave school at sixteen, do a secretarial course, work for a firm of Jewish solicitors, marry one of the partners and produce grandchildren for her. The Grants were observant Jews, but utterly materialistic, their motto "nothing but the best". They served gigantic meals in a suburban villa with a maid and a gardener and rococo furniture - repro, of course, because nothing second-hand would do. Grant's father yelled at waiters, and her mother became a virtuoso shopper, an expert on designer labels and how to match navy. When they moved her to an old people's home, her daughters found a collection of carrier bags worthy of the V&A. Grant admits to having inherited her mother's shopping prowess and confidence, and shopping together was their only bond.

The book opens with a shopping trip contemporary with its writing. Her mother needs an outfit for her younger daughter Michele's second wedding. Michele's little boy comes along; he likes shopping too. It is a trying occasion. There are triumphs, disappointments, fittings, rages, tears, and all the conversations go like this:

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"I've never had Jaeger in my life before."

"You must be joking. You've got a wardrobe full of it."

"Have I? I don't remember. Have I told you I've been diagnosed with memory loss?" "Yes. You've told me."

As they leave, she looks at her daughter and grandson. "'Just remind me,' she says. 'How am I related to you?'" By this time Mrs Grant has been in a Jewish home for the aged long enough to "settle" - in other words, to sink "into a bitter acceptance" of sitting in rows watching telly in an atmosphere of urine and air freshener. The book has taken us through her Liverpool prime to the grim time when the family lost its money, to a retirement flat in Bournemouth where her husband dies, then through the desperate period of trying to manage on her own, while knowing that often she didn't know where she lived or to whom she was talking. These things had to be concealed by lies. All the family lied. It was part of "putting on a face" which they needed to do to be the people they had become. "I thought all forms of lying were normal", writes Linda Grant, and she grew up deploring her family's "absence of honesty and authenticity". She has made up for it with this book which rings unbearably true.