Comedy is tragedy averted; tragedy is often comedy suppressed. Nothing is more powerful for a dramatist than a penetrating sense of the ridiculous. This George Bernard Shaw had in abundance. Comedy is his way of being serious.

“I am staggered by our current indifference to Shaw,” wrote drama critic Michael Billington in 2005. However, this indifference is comparatively recent. Until some years ago, there were usually one or two Shaw productions available to the theatre-going public. Then Shaw became unfashionable. The accepted cliché was that his talent was for lightweight entertainments that simply manipulated his characters as mouthpieces for Shavian opinions. Perhaps, though, these productions may have presented a rather different Shaw from the one that is being rediscovered. It is now clear that Shaw’s plays are about people, not puppets, and none more so than Pygmalion .

After Mrs Warren’s Profession was banned in 1893, Shaw resolved to write no more plays about social issues. He would concentrate instead on “plays of life, character and human destiny”. In Pygmalion, he achieved a brilliant synthesis of the comic and the serious. Of its comedic qualities, there can be no doubt: the first three acts culminate in the famous high comedy scene in which Eliza Doolittle, the cockney flower-seller Professor Higgins has undertaken to transform into an impeccably spoken lady through phonetic tuition, causes a social sensation with her notorious exit line, “Walk! Not bloody likely. I am going in a taxi.” The furore caused by that “bloody” at the first London performance in 1914 has continued to distract attention from what Shaw achieved in the two acts that follow. There is still laughter but the audience is invited to witness some complex psychological analysis. It brings the play closer to Strindberg and Ibsen – dramatists Shaw greatly admired and emulated.

So what does the seriousness of Pygmalion consist of? What is it about? Not, certainly, about phonetics, despite Shaw’s interest in the subject. Eliza asks Higgins to give her elocution lessons. If the play was simply about that, it would be irretrievably dated in our anti-verbal 21st century, where politicians want to be seen on television chatting away like any other man in the street. The play is about something much tougher (and paradoxically more contemporary): Higgins sets out to change someone’s personality. That is why it is called “Pygmalion”. In classical legend, Pygmalion was a sculptor who created a female statue so beautiful that he fell in love with his creation. He begged the gods to bring the statue to life. They did and Pygmalion married her. But, in Shaw’s version, Higgins does not marry Eliza. From the start, their aims diverge. She wants to be taught to speak correctly so she can get a job in a florist’s shop rather than having to sell flowers in the street. He, on the other hand, wants to create a “Duchess Eliza” – “my masterpiece”, as he calls her at the end. The last two acts develop this tension and the play ends in heartbreak.

What Higgins takes no account of is that his creation might have feelings of her own, and that in changing her he might have left her worse off than she was before. Eliza herself has no illusions about this: “I didn’t sell myself. Now you’ve made a lady of me, I am not fit to sell anything else . . . why did you take my independence from me?” But as she comes to realise, Higgins has actually increased her potential for independence: “I’ll advertise it in the papers that your Duchess is only a flower girl that you taught, and that she’ll teach anybody to be a Duchess just the same in six months for a thousand guineas.” The pupil has outdone the master. This is the crucial change Shaw makes to the Pygmalion myth: he brilliantly divides the dramatic interest between his two leading characters, “Pygmalion” Higgins and his creation.

But that in itself has led to problems for the play. In the film version, and in the musical masterpiece My Fair Lady, the two characters come together in a sentimental conclusion: the end is romance. Shaw was vehemently opposed to this, and when the seriousness of their relationship is uncovered in the last two acts, it seems amazing that anyone would think that they could end up together.

When Higgins says he will miss Eliza, Shaw is clearly leading his audience to expect a conventional romantic ending. And he does that in order to deprive them of it. What emerges most strongly from the final scene is Eliza’s sheer independence. She is, arguably, stronger than Higgins.

Throughout his life Shaw pursued laughter as a way of being taken seriously. So in act two of Pygmalion, just when the political temperature of the play is dropping, he produces a new character – Eliza’s father, the dustman, Alfred Doolittle. With his marvellous exposition of what it is to be one of the “undeserving poor”, Doolittle might have been simply a virtuoso comic turn but, with his verbal dexterity, he has more than a little in common with Prof Higgins. When Higgins asks if Doolittle is “an honest man or a rogue”, he disarmingly replies: “A little of both, Henry, like the rest of us. A little of both.” There speaks unaccommodated man, not merely a musical hall turn.

‘Pygmalion’ is the first of five productions in this year’s Peter Hall Company Season at the Theatre Royal, Bath. Previews begin on June 28, tel +44 (0)1225 448 844; www.theatreroyal.co.uk