Jaume Plensa with one of his works, Twins I and II, 2009, at Yorkshire Sculpture Park Photograph: Gasull Fotografia  On a surprisingly warm spring day in west Yorkshire the Catalan artist Jaume Plensa is watching over the installation of two giant mesh heads on the roof of a gallery not used to having things on its roof.  Elsewhere there are casts of the artist himself hugging cherry trees, silhouette figures spouting poetry ready to hang on the ceiling and alabaster heads contemplating, perhaps, deep matters of body and soul.  Over the next two weeks Plensa will continue installing what is the first major UK show dedicated to his work. He knows what he wants: "An artist must introduce beauty to people's everyday lives – it's our duty."  Yorkshire Sculpture Park, near Wakefield, is a long way from his huge studio outside Barcelona but the show is recognition for a Spanish artist whose international reputation just grows and grows. If you do not know Plensa's name, then the chances are that you'll know his work. It's everywhere.  In St Helen's there is the 20-metre high Dream, a dolomite-carved head of a girl, and on top of BBC Broadcasting House in central London there is Breathing, a 10-metre high sculpture that has become a memorial to journalists killed carrying out their work.  One of his most popular works is his Crown Fountain, in Chicago's Millennium Park, which opened in 2004. Works on the horizon include one in the central nave of Chichester cathedral – he beat Antony Gormley Mark Wallinger and other artists to the commission – and his first public art project in New York, a sculpture in Madison Square Park called Echo.  Plensa, like his fellow Catalan Joan Míro, is hugely influenced by poetry and there will be an enormous curtain of text running the length of one gallery with poems by his favourites, including Blake, Baudelaire, Ginsberg, Goethe and Léon Felipe.  Another work, In The Midst of Dreams, is a tribute to Oscar Wilde, referencing a letter the writer sent from prison where he states the three problems of being in jail: hunger, disease and insomnia. "That's the problems of life, they may be the only ones," says Plensa. "It is my little homage to Oscar Wilde, his letters are very inspiring. He put his life in danger to defend the concept of beauty which I'm also defending."  There are also self-portraits hugging cherry trees – "in my experience the trees grow faster. Maybe they feel loved or happy. A collector in Germany bought one and his tree is now double the size of his others."  He's well known, of course, in his home country but there is little public art of his there – a situation he says he is relaxed about. Plensa, who lived in Berlin and Brussels earlier in his career, admits he lives in something of a cocoon in his present home in Barcelona.  "Nobody knows I'm there, I like to be a little bit hidden." For now, his focus is on Yorkshire where new work will go on display with old.  "It is very interesting to have this dialogue with another environment. I'm from the Mediterranean so of course everything is different – the landscape, the light. It is a terrific opportunity and I'm pretty happy I have to say – I think it's working.  "To be here is a real honour – my ego is pleased."  • Jaume Plensa at Yorkshire Sculpture Park, 9 April-25 September
Plensa is staging his first big show in the UK but his work – Breathless, Dream and more – is already familiar here