The great Argentine writer Jorge Luis Borges once drew the line at translating Shakespeare. Speaking of the moment when Hamlet asks the ghost why it returns to haunt “the glimpses of the moon”, Borges commented: “I don’t think it can be translated. Perhaps the words can be translated. Certainly Shakespeare can't be translated.”

Yet, Daniel Hahn's book, If This Be Magic, argues that Shakespeare with every word changed can still be great, and can remain Shakespeare. Hahn recalls a hip-hop production of Romeo and Juliet he once saw, where the phrase “Do you kiss your teeth at me, fam?” proved to be a perfect translation of “Do you bite your thumb at us, sir?”. This example illustrates that translation isn't just about converting words, but about conveying the meaning and context of the original text. It's about finding the right words to get the point across.

Hahn's project is to show that Shakespeare's works can be translated into other languages without losing their essence. He reproduces chunks of Dutch, Russian, Welsh, Thai, Arabic, Japanese, and a dozen other languages, demonstrating how translators have tackled the challenge of conveying Shakespeare's meaning in different languages. For instance, in Māori, Lady Macbeth's question to her husband, “Are you a man?”, makes no sense at all, so the translator Te Haumihiata Mason renders it as something roughly meaning “Have you got balls?” – which is exactly what Lady Macbeth is asking. This translation works because it conveys the same emotion and intensity as the original.

The book also explores the annoyances and pleasures of translation in general. Hahn complains that the word “literal” is annoyingly overused to suggest a sort of “neutral” translation, which can't exist. He shows that, in many cases, a non-literal choice would be better. For example, when Mark Antony imagines Caesar's spirit to “cry ‘Havoc’”, the closest Portuguese word is the rather weak-sounding “devastação”; a better choice, Hahn shows, is “matança” (killing), because it's shorter and more easily shoutable. This choice makes more sense in the context of the play.

Each chapter addresses a different question translators face, such as whether to translate into verse or how to translate jokes. It's usually best, everyone agrees, to create an entirely new joke – “being faithful to the laugh”, as Hahn calls it. In a German Midsummer Night's Dream, to preserve the doggerel rhymes, we are promised not that Thisbe will be in “mulberry shade” but that she will be “hiding like a newt”. Translators might even embrace the possibility of a joke where none previously existed – which Hahn illustrates brightly by mentioning that the “sorting hat” in Harry Potter has become, in French, le choixpeau (the chapeau that chooses). This example shows that translation can be a creative process.

“In Shakespeare, people get sad with precision,” Hahn enthuses. And he is cherishably bitchy about certain literary “translators” who somehow produce new English versions of Chekhov or Ibsen without speaking the source language – the process being, as he surmises, “a sort of high-status prettying up of a so-called ‘literal’ translation”. He won't hesitate to call them out on it.

By the end of the book, Hahn has amply demonstrated not only the treasures of other languages but also the rich and strange inexhaustibility of Shakespeare himself. If This Be Magic: The Unlikely Art of Shakespeare in Translation by Daniel Hahn is published by Canongate, and it's priced at £25. It's a book that's worth reading for anyone interested in Shakespeare or translation.