In the late 1990s the indefatigable John Sutherland produced a series of entertaining books about puzzles in fiction (Why is Frankenstein's monster yellow? Where does Fanny Hill keep her contraceptives? Who gets what in Heathcliff's will?). The books were initially linked to reissues of novels in the Oxford World's Classics series, and I was struck at the time how beautifully these little inquisitions of Sutherland's, often on apparently absurd or marginal issues in the text, got readers reading again, with attention and interest. What Sutherland was doing, in effect, was smuggling serious literary criticism into an apparently superficial form of writing. Perhaps, in a sense, he was even re-inventing literary criticism. In this era of academic theorising and the downsizing of many of the broadsheet books pages it seemed a noble move. Could the same be done for poetry?

Poetry is a different case. While a healthy readership for classic and modern fiction has never been wholly lost, readers of poetry have in the last century dropped away like plague victims. There are occasionally revivals that don't seem to matter very much (stand-up poetry, perhaps) and there are still living reputations convalescing upon the history of being an A-level text (though poetry seems to have only a precarious foothold in many schools: I was told recently that there are now undergraduates in Oxford who have never heard of Ted Hughes). There are continuing heroic efforts by small publishers. But the recent defunding of the Poetry Book Society shows what the authorities really think of poetry. They don't seem to think much of it.

And one of the reasons for this is that poetry itself requires thinking. Some of its greatest effects rely on teasing and puzzling the reader. I wanted to get readers interested in some of these fundamentals. How do we know what the poem is about? How do we know what the poet is about? Poetry has designs on us, and it has a design of its own. We have to see the pattern in the carpet.

In our era, deliberate puzzling is a commonplace, almost an obsession. "I've put in so many enigmas and puzzles," said James Joyce about his monstrous poetic dream-novel Finnegans Wake, "that it will keep the professors busy for centuries arguing over what I meant, and that's the only way of ensuring one's immortality." Readers can get irritated with both the author and his attendant professors. At one extreme we sometimes wonder how we are meant to know if it means anything at all.

Much of the difficulty of what is still peculiarly called "modern poetry" can be put down to laziness, habit or pretentiousness (wanting to be another Joyce, especially). I needed to get to the root of simple puzzles in famous poems that would generally illuminate the process of reading. The way that we read poetry may be problematical, but it should always be pleasurable. And as Mallarmé put it, three-quarters of the enjoyment of poetry lies in discovering, little by little, what it means. You can throw some light on mere obscurity, but somehow you don't end up feeling enlightened.

I wanted answers to such basic puzzles about the subject as these: who is the "Emperor of Ice-Cream"? (Wallace Stevens was often pestered for clues about this poem, not least by the US Amalgamated Ice Cream Association, but he never admitted that it is something to do with Shakespeare and worms. Who is Ozymandias? Yes, Rameses II, but who was he really to Shelley?). Who is Crazy Jane? (This was not Yeats's first name for her: there is an interesting story here.) Sometimes the answer seems obvious. Tennyson's Mariana, for example, is a character in Shakespeare. But what happens when we try to read too much of her original role in a Renaissance play into her depressed Victorian monologue? There is a puzzle here, too.

The most condensed lyrics can have stories. We naturally look for them, but we have to work things out. Take Browning's "Meeting at Night", a poem which delights in concealing the story:

The grey sea and the long black land;
And the yellow half-moon large and low;
And the startled little waves that leap
In fiery ringlets from their sleep,
As I gain the cove with pushing prow,
And quench its speed i' the slushy sand.

Then a mile of warm sea-scented beach;
Three fields to cross till a farm appears;
A tap at the pane, the quick sharp scratch
And blue spurt of a lighted match,
And a voice less loud, thro' its joys and fears,
Than the two hearts beating each to each!

If you think there is no puzzle here, then ask what happens next? The encounter is clearly furtive. It is impossible not to feel that, like the waves, a woman is going to be startled from her sleep. Startled, moreover, not with reluctance but with a passionate response ("fiery") that is somehow conditioned by the light of the baleful moon reflected in the ringletted waves that represent her. A different sort of anticipation (definitely the speaker's this time) is suggested by the tactile, even sexual description of the boat's arrival ("pushing", "quench", "slushy").

In the second stanza, the matter-of-fact details seem designed to convey a different aspect of this story. A mile of beach and then three fields to the farm? Why therefore come by boat? Surely there must be a direct road to the farm? The tap at the window and the spurt of the match are both signals of the secrecy that must be maintained by making the least noise. Why is this? Why are the lovers conscious of the loudness of their beating hearts (louder than a whisper)? These puzzles are momentary. We realise that the love-making ("joys") can't take place here because of the possibility of discovery ("fears") and that therefore some kind of elopement is taking place. We can imagine the couple retracing the three fields and the mile of beach. Is it likely that after such a journey he will do so alone?

Of course, he might very well be alone. He might be making this journey every night, for all we know, and if so, it would be evidence of an heroic commitment to a forbidden or illicit amour (not unlike Browning himself insistently attendant on Elizabeth at Wimpole Street). If you choose that explanation you are perfectly entitled to do so. But my point is that the poem requires us to be alive to all these speculations: we speculate in order to resolve momentary puzzles.

Poems can also have their eyes on an idea while knowing that they must entertain us with "story". A good example of how we read a puzzling story when it turns out to be a symbolised abstraction (the subject deliberately withheld) is Stevens's "The Plot Against the Giant":

First Girl
When this yokel comes maundering,
Whetting his hacker,
I shall run before him,
Diffusing the civilest odors
Out of geraniums and unsmelled flowers.
It will check him.

Second Girl
I shall run before him,
Arching cloths besprinkled with colors
As small as fish-eggs.
The threads
Will abash him.

Third Girl
Oh, la . . . le pauvre!
I shall run before him,
With a curious puffing.
He will bend his ear then.
I shall whisper
Heavenly labials in a world of gutturals.
It will undo him.

With as much story as this, based on motifs from folk-tales, we are close to allegory. But allegory (where Spenser's Red Cross Knight is the Anglican church, Una is the true religion and her protecting lion is England, and so on) is usually a quite deliberate performance that asks to be decoded. Stevens's giant is an unarguable familiarity, a constant in all human existence. His version of Death as a clumsy murderous peasant somehow to be "checked", "abashed" and finally "undone" by Beauty is so brief and powerfully dramatic, that we barely reflect on the outrageous claims it makes, or the curiously elitist presentation of that familiar triad Nature, Art and Poetry.

This elitism, constituted of an extreme fastidiousness and refinement of taste ("civilest", "unsmelled flowers", "besprinkled with colors") and a dash of salon patronising ("le pauvre!"), doesn't seem likely to us to have any effect whatsoever on the whetted hacker of Death. Indeed, once we have solved the primary riddle-like puzzle of identifying the giant, this ineffectiveness becomes the core of the secondary puzzle: what is Stevens really saying about the power of the aesthetic faculty?

We sense an irony in the Lilliputian heroism of the three girls. Take the phrase "arching cloths besprinkled with colors". It's an odd way to describe a painter's canvas. It's much more like the way you would describe the preparation of a cloth sprinkled with chloroform in an attempt to "anaesthetise" the giant, a hopeless prospect given his size and the fact that she is running ahead of him. It is in fact knowingly hopeless: "arching" is itself arch. There is irony, too, in the final postulated triumph, since in the human language of poetry gutturals (sounds produced in the throat) must obviously be employed as well as labials (sounds produced by the lips). The evident truth of this preference for labials has, incidentally, recently been concisely explained by David Crystal in this newspaper: "You're in a spaceship approaching a planet. You've been told there are two races on it, one beautiful and friendly to humans, the other unfriendly, ugly and mean-spirited. You also know that one of these groups is called the Lamonians; the other is called the Grataks. Which is which? Most people assume that the Lamonians are the nice guys. It's all a matter of sound symbolism."

Stevens's Giant is obviously a Gratak, but this isn't the end of the story. Just as poetry must use worldly gutturals as well as "heavenly" labials, so our sense of the value of human life must also encompass the fact of death. Elsewhere, Stevens unequivocally attributes our sense of beauty precisely to the fact of mortality  "Death is the mother of beauty". And the girls run before him not only because he is in murderous pursuit, but because they could not be aesthetes at all without the sense that death will inevitably catch up with them. In Stevens's philosophy the giant is not only whetting his hacker; he is whetting our transient appreciation of beauty.

The point of all this will dawn upon us sooner or later, but sometimes the most alert and interested readers of poetry simply don't notice the obvious, even in their favourite poems. This inattention can be part of a rapt reinvention or appropriation of the text. We sometimes want to see a poem in our own terms. We misread it or misremember it. Does this matter?

Misquotation can open up interesting questions that the poet may have thought that he had avoided or disposed of. Take Larkin's celebrated last line of "An Arundel Tomb": "What will survive of us is love." The line is often quoted in any case as a resounding emotional comforter, forgetting that Larkin only introduces it as an "almost-instinct" that is only "almost true". Not much comfort there, then, from the old bachelor, it is commonly said. But what is one to make of Antonia Fraser talking on the radio about her recently published memoir of her marriage to Harold Pinter and quoting the line as "All that remains of us is love"?

These substitutions raise the interesting puzzle of what Larkin might have thought the survival to consist of (and in particular, where). I refer to substitutions in the plural because to begin with Fraser has replaced with an absolute "all" what in Larkin's poem is something like a question tentatively answered: "What will survive of us?" "What will survive of us is love." Her absolute doesn't seem much, though. "All that remains" is close in sense to Shelley's "Nothing beside remains" in his sonnet about Ozymandias. The glum sense of her version of the line is, in fact, "the only thing that remains of us is love". It is depressingly like a puddle where something has melted, whereas the poet's words deliberately and almost triumphantly invoke survival. To survive is (from the late Latin supervivere) to live after death. You might have thought that Fraser, as a divorced Roman Catholic who needed a ceremony to sanctify her union with the Jewish Pinter, would pick up on the word "survive", the resurrection of the body, instead of substituting the dismal "remains". Larkin is writing about a tomb, after all, where the actual remains were laid. Survival is an altogether grander concept.

But her mistake sends us back to the poet's puzzle. Where does love survive, if it does at all? Not in the earl and countess's bodies, clearly. Nor in the tomb itself. Nor in our facile human presumption of it, given that we readers are like the "altered people" who visit the tomb, no longer the "friends" who knew them. But it must, if it survives at all, be something that the poem itself recreates, by adopting and elaborating their intended "blazon". In that case, the actual words of the poem become of sacred importance. Her mistake might be thought forgivable in a broadcast interview, but it turns out to be there in her book as well.

There are puzzles in the very titles of poems. No one really seems to know, for example, why Coleridge calls his lime-tree bower (a sweet-smelling sheltered writing space in his neighbour's garden) a "prison" in his poem "This Lime-Tree Bower my Prison". Or at least, the easy answer isn't the best one. (But puzzles are like that.) Some title puzzles strike at the heart of what giving titles to poems is all about in the first place. What is really going on when a poet calls a poem "Untitled"? Another example: there are multiple titles and macro-titles for Browning's "Porphyria's Lover" that affect the way in which we read it. The poet can change a title and not realise what a profound effect this can have, as Browning did, bequeathing us another puzzle. And there is a further Victorian poem, perhaps the most famous Victorian poem of all, which doesn't really have a title as such, though most readers will not have realised it. However, the fact highlights a puzzle in the poem itself: what is "In Memoriam" actually about?

And why is the title of the most celebrated modernist poem quite frequently misquoted by those who particularly should get it right? I'm not referring to the fact that for much of its early existence in Eliot's mind the poem was to be called "He Do the Police in Different Voices." It was soon enough known as The Waste Land, and The Waste Land is what it assuredly is. Why, then, do so many people call it The Wasteland?

When the error is pointed out, it is often felt to be a venial slip of the pen, as though the two titles were more or less identical. They are not.

It is perhaps worth quantifying the error, or at least giving some idea of its extent not only in common parlance but also in professional and academic contexts. I'm not simply referring to the errors of students in their essays and examinations, although the most abundant examples are found there (I would say from my own experience that perhaps three out of ten students habitually get it wrong). In fact, the poem was so miscalled from very early in its existence, as when Bertrand Russell told Ottoline Morrell in 1923 that he was particularly excited to get hold of "Eliot's Wasteland". The mistitling occurs widely in print, and evidence of it in official contexts could be freely collected, for example in the promotional leaflet for Icon Critical Guides to Literature (distributed by Penguin Books), where in "Forthcoming Titles for 1999" a poem called "The Wasteland" is enthused over by Rachel Bowlby; or in the lively literary periodical the Devil (1999), where Andrew Motion so refers to Eliot's poem (and again, 10 years later, in the Guardian); or in Germaine Greer's lecture "The Name and Nature of Poetry" (Guardian Review, 1 March 2003,); or in a piece about Henry Reed by Adam Phillips in the Observer Review, 28 October 2007.

Of course, these writers are in the hands of interviewers, journalists and copy-editors, and are not to be blamed. Or are they? Probably these interviewers, journalists and copy-editors were themselves only recently students whose orthographical errors were silently passed over by their busy teachers and examiners and therefore continued to be carried, like undefused bombs, into their unsuspecting literary careers.

Finally, if you want to hear Eliot himself reading his poem in The Caedmon Treasury of Modern Poets Reading Their Own Poetry you will find it listed on the record sleeve as . . . "The Wasteland".

It should be possible to end the solecism forever by distinguishing clearly between wasteland (a plot derelict or not yet built on) and waste land (land laid waste, by an army, perhaps, or by a failed harvest). A property developer might have his eye on wasteland, and there is after all a fair amount of it in Eliot's poetry. These are the civic interstices across which newspapers blow or rats scurry. Wasteland is waste as bogland is boggy or grassland grassy: it is an area of a size unspecified because the size is unimportant compared with its condition. "The Wasteland" invokes a specific area as yet unspecified. The implied plural "Wastelands" would have been an interesting alternative title, had Eliot wished to symbolise the dead souls of his city-dwellers. In the singular, "Wasteland", by contrast, might be a section of a report on urban conditions. All these alternatives are quite opposed to the sense of the devastated patria inherent in his use of the singular "Land".

This waste fatherland is at the heart of the poem's final meanings. It involves the crucial role of the central figure of the poem, the blind prophet Tiresias, and much of the poem's Grail myth. But Eliot himself created another puzzle when noting the centrality of Tiresias's consciousness, recounting the reasons given in Ovid for the prophet having been blinded by Juno, but saying nothing about his role in Sophocles. Tiresias's bisexuality is significant in Eliot's scheme of things, but not so important, I think, as his unique understanding of the significance of the blighted harvests of Thebes, and of the guilt of Oedipus. Giving the poem its correct title helps us to see this.

I'm interested in riddles and submerged metaphors, and why we feel that the poetical imagination is sometimes missing in Augustan poetry. There are various ways in which the reader might distrust the poet (can we really believe that a poem arrives in a dream or at the dictation of a spirit over the ouija board?). I'm interested, too, in various examples of involuntary misunderstanding (Milton isn't gushing when he writes that Eternity is "perfectly divine"). Readers who find poetry difficult should be comforted by the knowledge that even the most astute reader, including every critic, can find it difficult. A single word may contain a puzzle whose unwrapping makes plainer the entire design. The pleasure of solving such a puzzle (in Mallarmé's sense) is part of what reading a poem is. Which is why poets on the whole would rather do the Guardian crossword than write lyrics for the latest boyband.

It is in the very nature of poetry to be forever setting up problems of meaning that require an alert solving response in the reader, and that this is one of a poem's greatest pleasures.