To visit gardens in Northern Italy is to experience a feast of contrasts - brilliant hot sunlight versus carefully constructed cooler shade; meticulously clipped topiary designs and wilder woods; architectural pomp and circumstance and quirky jokes and entertainment; greenery and splashes of colour; sun-baked earth and water; and enclosed spaces opposed to dizzying panoramas. Their history is a cycle of opulence, decline and renewal.

Catch it while you can – an exhibition celebrating one of garden history’s greats is closing next month. It’ll mean a trip to France, but it’s worth it to see the venue alone. Held at the Palace of Versailles, André Le Nôtre in Perspectives 1613-2013 presents the fruit of the latest research on the man who not only created the iconic gardens at Versailles but whose work continues to influence urban planning and garden design today.

Gleaming gold and enmeshed in a metal frieze of black and silver circles evoking the city’s industrial past, the new Library of Birmingham bestrides the central Centenary Square, part luxury ocean-going liner and part giant Lego construction in design. Inside blue-lit travelators ferry visitors up and down through cavernous book rotundas.This strikingly different design by Dutch architects Mecanoo also includes three unique and distinctive roof gardens which encompass elaborately patterned parterres and potagers, undulating landscapes of grasses and flowers and wildflower meadows.

It’s not every exhibition that can boast its own specially commissioned pop-up garden, but Georgians Revealed, at the British Library until 11 March 2014, is an honourable exception. Installed on the usually rather austere forecourt of the BL, the Georgeobelisk, instigated by Cityscapes and designed by Todd Longstaffe-Gowan, is a quirky overture to an exhibition that asks ‘never mind the Romans, what did the Georgians ever do for us’?

The last RHS show of the year, Shades of Autumn at the RHS Horticultural Halls in London, bid farewell to British Summer Time with a burst of seasonal (and sometimes not so seasonal colour – tulips in October anybody?), and with a powerful affirmation of garden design creativity.

Combining horticultural know-how with artistic flair, Tony Heywood and Alison Condie are using their unique style of urban gardening to establish eco-friendly design and practice on the Hyde Park Estate.

There was a time when hi-tech entertainment in your back garden meant struggling to find a signal on a portable radio, or pushing the telly out on to the patio during Wimbledon. But today gardens can be as hooked up as the most gadget-filled living room – with all the mod-cons you’d expect to find inside the house, and more.

Over the last few years evidence has mounted about the alarming rate at which children are losing touch with nature, and the damage this can cause to their overall well-being.

Modern life is increasingly hectic and, paradoxically, the more we need the solace of nature, the less time we have to spend outdoors. When we do finally get out there, tending the plants might not be the first thing on our minds. Here, though, Chelsea gold-medal winning garden designer Kate Gould has plenty of tips and tricks for creating a great garden without the graft.

Once upon a time, you needed fields, barns and possibly a tractor to live the country life. But not anymore. In her new book The Rurbanite, Alex Mitchell shows you can grow vegetables, keep ducks and commune with nature right in the heart of the city. And, as she explains here, you don’t even need a garden to get growing!