Nominated as one of the New Yorker's top 20 American authors under the age of 40, Rivka Galchen has one novel behind her and a string of stories that have been published in the New Yorker, Harper's and the New York Times.

On the evidence of her first collection of short stories, one can certainly see why her voice would catch the attention. Whether or not it will survive or indeed thrive as she matures is less easy to predict.

The opening story, The Lost Order, is well placed as an introduction to her mannered style, being the most rounded, satisfying and least unnerving of the 10 stories here. Told in the first person, as are all but two of these tales, it describes a woman who is currently at home, without a job, who picks up the phone to hear a man barking an order for a Chinese takeaway. Startled, she promises it'll be with him in 45 minutes, before hanging up and continuing with her daydreaming.

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In the rather hectic, solipsistic manner that quickly becomes familiar as these stories unreel, the narrator pulls the reader into her neurotic and unhappy existence, where the chirpy voice soon reveals itself as a cover for profound insecurities, albeit drolly recounted. Venturing outdoors, she encounters a pair of delivery women. "'I've never seen a woman working UPS delivery before,' I say. 'And now here you are - two of you at once. I feel like I'm seeing a unicorn. Or the Loch Ness monster. Maybe both, I guess.' There's a bit of quiet, then."

The Lost Order is a gem of a story, knowing, witty, and poignant, with an ending that ties up everything that preceded, and leaves the future tantalisingly unknown. Thereafter, however, with a couple of exceptions the stories are less sure-footed, more ragged.

There's one about a woman who discovers she has grown a third breast on her back. When she asks a doctor if it can be removed, the doctor's reply is almost as unsettling as the condition. In another, a woman gets home late to see her apartment shrouded in darkness. She always leaves the lights on, but as she stares, expecting to see burglars, she is startled: "Some ... thing was emerging from the darkness there. At first, it looked like a nothingness that had acquired an outline on the cheap. But as it descended - it was descending - it became more fully ontologically realised. It was my ironing board."

Piece by piece, her belongings are escaping. She is strangely untroubled, even though she had earlier admitted that, while she likes people, "I prefer the taciturn company of my things. I love my things. I have a great capacity for love, I think ..."

By turns thoughtful, whimsical, surreal and sad, American Innovations is the work of an electric imagination, of the sort owned by those who are a layer or two short of a full skin. Galchen's descriptions of characters are indelible, as when she talks of a school chum who had "a cheerfulness whose border none of us had encountered". The parade of individuals who cross these pages is pungently evoked, and yet the voice telling the stories does not vary, from one story to the next. Are they all the same person? They certainly share similarities: an interest in science, difficult mothers, a long-dead father who crops up unexpectedly, in dreams, or otherwise.

Inhabiting a universe that lies somewhere between stern, bleak reality and limbo, or even the afterlife, American Innovations is a showcase of sometimes brittle, often clever, occasionally tedious stylishness. Nor is it devoid of content, although at times its tricksiness and laboured insouciance grow wearisome.

By its end, this reviewer felt like one of Galchen's narrators. Faced with a row of photos used to help those with autism recognise what other people are feeling, she reflects: "I could tell what emotions I was supposed to see, sure, but to my heart, they all read the same, they all looked like cries for help."