Deck quoits and ballroom dancing are not the only forms of entertainment you'll find on a cruise ship. David Lister sails the Mediterranean on Minerva II, enjoying expert lectures on art and architecture, with a spot of Mozart added for light relief

It's not often that you book a holiday to find that your ticket arrives with a reading list. On my recent Swan Hellenic Discovery Cruise, I had the choice of working my way through Oxford University Press's Archaic and Classical Greek Art or Byzantium: The Early Centuries, or 11 other worthy tomes. By the time we actually set sail I felt that I had earned the break.

Cultural cruising sounds horribly like looking for a date in an art gallery. But think art and water: sailing round the Aegean and the Med, with the usual pampering that a cruise implies, but crucially with lectures on board from scholars, curators and authors before visiting the classical sights, ancient towns and monuments.

Such cruises, nurturing the mind as well as the body, have been available for some time and have tended to attract the affluent and those of pensionable age. But now Swan Hellenic, the leaders in discovery cruises, has introduced a new ship with facilities that could encourage a younger age-group seeking cultural stimulation.

Not that the present clientele aren't themselves stimulating. I cruised for a week on the Minerva II, Swan's new ship, its main lounges furnished like a country house with gilt-framed pictures and scented flowers, and encountered a passenger list straight out of the pages of Who's Who - former ambassadors and diplomats, museum curators, judges and academics. The classical music outfit Terzina, playing on board, credited the arranger of one Mozart piece and were stunned to be told that, at the age of 92, she was sitting a few feet in front of them. The art critic Martin Gayford, who was one of the excellent guest lecturers, entered into a debate on Le Corbusier with one passenger, only for his antagonist to mention, crushingly, that he had been a pupil of Le Corbusier.

What I discovered on the cruise, however, is that there is no reason why a holiday incorporating cultural enrichment, a spot of pampering and physical improvement should not appeal to a younger age group, too. And I stress physical improvement. The Minerva II has a state-of-the-art gym with a personal trainer. I shall not easily forget how much more pleasurable it is to ride an exercise bike when the view in front of you is a massive picture window facing the breathtaking sea approach to Venice. Daily classes in yoga, pilates and flexibility also take place in the gym, with a range of health and beauty treatments in the adjoining beauty salon.

It's a strange thing, a cruise, a sort of parallel universe where you don't feel bound by the norms of dry land. Which is a philosophical way of saying that I left sexual stereotyping on shore and treated myself to a facial, having for years wondered what they were all about. Having tried one, I still don't understand.

The ship also contains more comprehensible diversions: a library, a small swimming pool, a golf practice net and table tennis on deck, jacuzzis, thalassotherapy pools and endless sunbathing space. The formidable ratio of 300 staff to 600 passengers means there is no such thing as waiting for drink or meals. The service was outstanding, though the food could be better. Evening meals, served in four restaurants, one in the open air, needs to go up a notch to match the other facilities and service.

At night, the entertainment was live classical music from Terzina, and a smashing and much travelled outfit called the Shakespeare Revue, which offers sketches, jokes and songs as well as pastiches of the Bard. Late night sees a jazz band, again of high quality, mixing lounge music for dancers with improvisations that show a technique more suited to Ronnie Scott's where, it emerged, they do indeed play. The venue for this, the Orpheus Room on the 10th deck, is a stylishly designed late-night bar, intimate with all tables a stone's throw from both band and bar, yet facing panoramic windows so that one never forgets where one is.

But essentially this cruise is about something quite different: learning while you holiday. And it offers a remarkably enjoyable way to learn. A daily programme is put through your cabin door detailing the lectures and places to be visited. So, for example, before looking round the old town of Dubrovnik (almost totally restored after heavy shelling in the Balkans conflict, but still with tell-tale shrapnel on church walls), I listened to a talk on Byzantine art from Lady Sophie Laws, a former lecturer in theology at King's College, London. Her knowledge of the area, particularly of Greece, is not just second hand - she and her husband, the appeal-court judge Sir John Laws, have a home on a Greek island. It seemed to sum up the joyous intensity of the cruise when she, a passenger and a Greek guide had a heated debate with the captain on the bridge over whether the icon of St Nicholas on the ship should be facing the sea or not.

The churches, monasteries and other religious sights on our stops were also made more interesting by lectures from Mark Santer, the former Bishop of Birmingham. His talks at times strayed away from buildings and on to ways to resolve religious differences, a topic that gained urgency as we sailed from Greece to Croatia.

The old Greek town and hillside of Monemvasia (a great benefit of cruising is that one can see some great relics, such as this, which are difficult to get to by road) was enhanced by the classicist Colin Badcock. He explained the origins of Greek theatre, how it arose from the countryside cult of the god Dionysus, the flat earth serving as stage, the audience sat on the nearby hillside; how the birth of drama came when the "answerer" to the Chorus dropped narration and impersonated a character. He became an actor, Hippocrates - the hypocrite and pretender. A tent represented the background, and the Greek word for tent was "scene".

As we approached Venice, Martin Gayford's talk about its art and architecture gave illuminating insights, explaining with slides the importance of light to Byzantine sensibilities as light in art was a metaphor of spirituality. Suddenly I had an enhanced sense of the cultural complexity of the Mediterranean, the layers of Byzantine, Italian, French, British and Greek influence; why early Christian churches liked to use mosaics; how Venice took relics from Thessalonika; that our word "barbarian" comes from the Greek word for their "contempt" for the Macedonians. And I wondered at Colin Badcock's observation that Byzantium, Constantinople and Istanbul were great empires, yet none received a mention in the British education system.

And culture isn't just a matter of art and history. The food writer Frances Bissell was among the guest lecturers. She made a determined case that food speaks of our history and geography, of empires and conquests, families and tradition. Almost inspiring one to stay on board for the next leg of the cruise, she said: "When I eat fenkata in Malta, sutlac in Istanbul, koshari in Alexandria, paella in Valencia, gelato in Naples; when I join the jostle on the quayside to examine the fish being unloaded, as I pick out the most fragrant melons, the ripest tomatoes and freshest lemons from the market stall, I am no longer an outsider, I belong."

The cruise round Greece and Italy was just one segment of a year that will take Minerva II across the Atlantic and around South and Latin America, the Amazon and the United States' southern states, with guest lecturers speaking on everything from Mayan civilisation to Caribbean wildlife and New Orleans jazz.

Most people seem to cruise for a fortnight, but you can do a week, as I did, or much longer. One American gentleman, either in love with art or in need of a facial or two, has just booked seven months on board. A standard cabin costs just over £2,000 for a week, a deluxe cabin with balcony £2,700, and an "owner's cabin" - a veritable suite in which you can entertain your friends - £3,700. But there's also a cheaper way of doing it - a cabin without window for £1,600. With large mirrors giving the illusion of light, and no great need to spend much time in your cabin, this would not be a bad way of getting a first-class cruise for a smaller outlay.

Certainly, if you want seclusion, you don't need to stay in your cabin. The ship is so large that I could always find somewhere private, whether strolling around the top deck or having a steam bath and jacuzzi. Only one area was closed off - the very front end of the ship. I was told that ships all over the world have taken similar action. It seems that after the film Titanic, an endless stream of young couples had wanted to pose as Kate Winslet and Leonardo DiCaprio - a dangerous declaration of love in a high wind. My fellow travellers on the Discovery cruise could no doubt explain how the ancient Greeks would have staged such a romantic ritual.

Reservations: Swan Hellenic 0845 355 5111