In 2003, English writer James Lasdun taught a fiction workshop at a college in New York City. The star of the workshop was a woman in her 30s he calls "Nasreen", who was working on a novel based on her family's experiences in pre-revolutionary Iran. "There are seldom more than a couple of students in any workshop who seem natural writers, and they aren't hard to spot," Lasdun writes in the early pages of his memoir, Give Me Everything You Have: On Being Stalked. "It was evident to me, after a few paragraphs, that Nasreen was one of them. Her language was clear and vigorous with a distinct fiery expressiveness in the more dramatic passages that made it a positive pleasure to read."

Two years after the workshop ended, Nasreen emailed Lasdun about a finished draft of her novel. An epistolary relationship gradually emerged in which the then fortysomething Lasdun played a kind of mentor role. Soon, however, the frequency and amorousness of her emails became unsettling  Lasdun was happily married  and he began to try to detach himself from the correspondence. Nasreen did not relent, and the tone of her messages became increasingly dark, angry and, eventually, unhinged. The "distinct fiery expressiveness" of her language built towards an inferno of vengeful hatred.

This is the starting point for Lasdun's memoir, which is his attempt to make sense of (and defend himself from) the consequences of that relationship turning sour. Over a period of seven years, Nasreen hounds him online. Her modus operandi involves diffusing toxic rumours of sexual harassment and plagiarism  in Amazon reviews of his books, Wikipedia entries and the comments sections of his articles. She contacts university and publishing colleagues in order to damage Lasdun's relationships with them. Her emails, meanwhile, become increasingly characterised by an ugly and insistent antisemitism: "I say if I can't write my book and get emotionally and verbally raped by James Lasdun, a Jew disguising himself as an English-American, well then, the Holocaust Industry Books should all be banned as should the films."

The memoir's first third or so is as unsettling as anything I've read about the internet's awful capacity to facilitate the dissemination of hatred. Much of this has to do with a strong sense, in Nasreen's case, of the total arbitrariness of this hatred. Apart from remaining unresponsive, Lasdun seems to have done nothing to provoke her; she might just as well have focused on any other writer, any other person. But perhaps the book's most terrifying revelation is the idea that all that is necessary for a person's life to be made utterly miserable is for another person to want this badly enough, for whatever reason. The internet is the genie that grants such poisonous wishes. Nasreen's campaign of harassment and character assassination amounts to a kind of frictionless sharing of malice.

The book is, among other things, a fascinating meditation on the malleability of identity in the online age, on the ease with which the truth about individual lives can be publicly distorted. Lasdun presents this as a kind of cultural atavism, a return to a pre-modern situation where social arrangements were dependent upon trust and hearsay, and where a stain on one's honour could be catastrophic. "The internet emerged," he writes, "and with it the arbitration of reality began to pass back from the realm of verifiable fact to that of rumour and report, from the actual to the virtual There was the private self, still, but for anyone who interacted with the world there was this strange new emanation of yourself, your internet presence, and it was by this, increasingly, that others knew you and judged you."

Perhaps because Nasreen's presence in the narrative is a disembodied one, we experience her as a kind of evil spirit in the online ether, a curiously spectral source of malediction and misfortune. And Lasdun is acutely aware of the ease with which she therefore lends herself, as a "character", to these sorts of mythologising and essentialising impulses. (He is oddly explicit about his lack of interest in mental illness as a means of accounting for the actions of his tormentor; psychological explanation is a literary blind alley he's reluctant to set foot in.)

One of the book's most fascinating aspects is the extent to which it's a story about a writer struggling with, on the one hand, a version of himself created by another writer and, on the other, his own need to make sense of that other writer as a character. Questions of culture and gender inevitably become central to this game of shifting mirrors. "By a certain point," he writes, "we were both, in effect, creating or re-creating each other in the image of our crassest fear, our most cravenly stereotyping fantasy: the Demon Woman, shall we say, and the Eternal Jew." If it weren't completely factual, in other words, this story could easily have wound up being a little too metafictional for its own good.

At times, in fact, the book reads like an oddly literal rendering of Jorge Luis Borges's short prose piece "Borges and I", in which he explores the deepening alienation between his own public and private selves. Lasdun finds himself having to confront the public version of himself that Nasreen has created  a character called "James Lasdun"  whose presence constantly threatens to compromise and obliterate his own. "This other version of me," he writes, "so much more vital and substantial than I felt myself to be by this time, had completed its usurpation of my identity and was running amok."

As intriguing as this material is in itself, it's Lasdun's deviations from it that make for such an odd and original work of nonfiction. There are long, idiosyncratic digressions in which he views his situation through various literary lenses  readings of Tintin, Sir Gawain and the Green Knight, Macbeth and the poetry of Plath. Literature provides an oblique line of approach to the awful complexities of his predicament, to Nasreen's apparently motiveless malice. And there's a long interlude where the book detours into a travel narrative in which a trip to Jerusalem becomes an occasion for historical meditations on antisemitism. What is finally most riveting about this strange and unsettling book is not the grim fascination of Lasdun's situation; it's the moral intelligence and intensity with which he examines it.

Towards the end of this book, the author lists some reasons why perhaps he shouldn't have written it. There's his wife and family to think about. There are legal considerations  it being a true story of an ongoing conflict  and ethical ones: "The necessity of using private emails in a story about accusations of plagiarism and violations of privacy was an irony I was going to have to come to terms with." And there's something else, to do with taste, trust, the good opinion of others. "Even if I settled all these matters for myself, there were bound to be readers  honest ones as well as the professionally offended  who would object to the very notion of such a book." Can a reviewer count as an "honest reader"? Aren't we just as tarred as all the memoirists by Janet Malcolm's famous condemnation of the journalist as "confidence man" and "morally indefensible", "too stupid or full of himself to notice what is going on"?

The story starts in 2003. James Lasdun, a respected poet, novelist and short-story writer, born 1958 in London but resident in upstate New York, is teaching a fiction workshop in "a place I'll call Morgan College". Among his students is "a woman I'll call Nasreen  in her 30s, quiet and reserved". Nasreen is working on a novel, a family epic set in Tehran in the 1970s. Her writing is "clear and vigorous" and the professor is "impressed". He's impressed, too, by her "unflustered" reaction when he says so. That's "the mark of a real writer", he thinks.

And so the professor and the student start talking. She's funny and self-deprecating, with looks that convey "the same undemonstrative confidence" as her prose. She is Iranian and writing autobiographically  her family came to the US in 1979. Her jeans "look expensively soft and faded". Her face is "fine-boned, with delicately interlocking features" and "the same sallow olive complexion as my own". And for the next two years or so, that's it.

In 2005 Nasreen emails to ask Lasdun to look at a finished draft of her novel. He can't do it but introduces her to his own agent and asks her how she's getting on. She's in New York City with a boring day-job and has just split up with her fiance. Lasdun, meanwhile, is settled, established, happily married with two children. He sends news of his pet cockatiel and his plans for his vegetable garden. "I began to think of her as  a brand-new friend." Nasreen's emails start getting flirty and "slightly manic". Lasdun makes it clear that he isn't looking for affairs or intrigue; the mail he gets back is "lucid, gracious".

But then Lasdun emails Nasreen with two questions. "The first was a general one about what it was like for someone from the Muslim world to be in New York in the immediate aftermath of the 9/11 attacks." The second was about "veils, burkas, yashmaks, niqabs, chadors [which] had been a source of imagery for me since my first book of poems in 1987". "A deluge of fraught, breathless veil-related emails followed  insistent, unstoppably amorous."

Over the next months, Nasreen's mails become delusional, with "a new tone, a sort of exhibitionistic boisterousness" and weird, paranoid plotlets in which "the motifs of sex, gender, race, money and Middle Eastern politics mingle in strange ways". Finally they become hideous, abusive, antisemitic. "How fucking crazy Jews are these days  I can't say that but hundreds and thousands of Arabs can die in silence? I don't fucking think so, sir." "I think the Holocaust was fucking funny and about as hilarious as the Holocaust industry." "Boycott this man, for God's sake. He's the reason behind terrorism." Lasdun's analysis is succinct. "I, as an Anglo-American Jew, a family man, a published author, a middle-aged male in a position of power (at least from her perspective), was the axis of, shall we say, 'virtue', while she, in her own mind at least, was the lone jihadi." Though Nasreen puts it this way: "I'm a real person who's spent her whole life trying to survive because I live in a fucked-up sadistic country."

Mails go to Lasdun's agent and university employers. Wikipedia is hacked and words inserted: Lasdun's stories linger, the entry says, "like a fart". An ingenious delusion imagines Lasdun as a "literary racketeer", stealing Nasreen's ideas and selling them on to other Iranian-American women writers, "most of whom happened to be Jewish". Lasdun searches for what remedies he can. Calls to the FBI meet only with "mildly puzzled indifference". An NYPD detective is interested, but the threats are never specific enough. I kept wondering if this book was really fiction presented as memoir for some reason, but it doesn't seem to be: at one point, Lasdun writes about an idea he had to change round the time-scheme, only to abandon it. "I realised this strange narrative could work only if I kept very strictly to the facts."

But this is an extraordinarily odd and disturbing story. Like Nasreen, Lasdun is a "real writer", "someone for whom words are a source of primal delight". The poet in him is skilled at following tiny snags of thought into marvellous, rich mini-essays: on Gawain, DH Lawrence, Patricia Highsmith's Strangers on a Train. Himself the author of brainy, sophisticated noirs (Seven Lies, Besieged), he's brilliant at using folk and modern narrative forms to enliven each other  there's one particularly fine story, about a Palestinian housepainter whose son dies blowing up a supermarket, with an even worse sting at its end. Lasdun's inner critic also knows how to show his workings. There's a very nice bit on the pull of trashy thrillers  the "dreamlike, redistributive accuracy" with which they dramatise widely felt forms of pain and grief.

And yet the book as a whole is skewiff, with both far too much information in it and not enough. On the too-much side, there's the lavish quoting of Nasreen's awful emails, and the way Lasdun's story seems almost to fan their flames, affirming and enlarging their grandiose view of their author as a "verbal terrorist", a practitioner of "asymmetric warfare". I could also have done without some of Lasdun's own psychic self-dramatisations, the "ruins of ancient prejudices  like  decommissioned artillery emplacements" he finds in his own mind. Hearing a man speak Arabic on his phone, he thinks about "the nightmarish aura" of the al-Qaida terrorist Abu al-Zarqawi. Chatting to his son about Tintin, Lasdun muses on "the soft racism that pervaded the world of my childhood"  "okay" because "largely without malice", or so he claims.

At the same time, the story is also full of gaps. There's little, for example, on the possibility (the probability, surely) that Nasreen is in terrible distress: "borderline personality" is mentioned, as are "chemical imbalances" but Lasdun isn't interested in a diagnosis, preferring to see her behaviour as motivated by "a malice that  simply is". (At "odd moments I have sensed that this is a failing on my part," he muses, "maybe the precise failing that laid me open to her siege in the first place.") Connected to this is an almost total lack of self-irony. "Here I was, a standard-issue liberal with unimpeachably correct views on everything, casting the shadow of some leering, reactionary bigot." "How does a middle-aged man  fight a young, struggling Iranian woman filled with the sense of her own marginality, without feeling (and looking) like a jerk, a pussy, a chickenhawk imperialist, a 'fucking faggot coward'?"

As the story progresses, it becomes less about Nasreen and her emails and more about Lasdun and his patrimony, as the son of the architect Denys Lasdun and as a non-religious Jew. Right at the end, he goes to Jerusalem to write about the Hurva, the ruined synagogue, the controversial rebuilding of which was completed in 2010. "The question of where honest criticism"  honest criticism, again!  "of Israel ended and antisemitism began had started to interest me greatly," he writes. A woman offers to take him around a Palestinian refugee camp, then seems to edge away. "This in turn awakens an ancient insecurity of mine: is there something about myself that I simply don't see?"

I am not myself well read in anything to do with Israel or Palestine, Jews and Muslims, anti-Zionism or antisemitism. But again and again, I found myself remembering a remark the scholar Jacqueline Rose made last year to the Guardian: "Victimhood is something that happens but when you turn it into an identity you're psychically and politically finished." Good advice for Nasreen, wherever she is. Good advice, perhaps, for Lasdun, too.