So, Anyway by John Cleese is not an autobiography in a conventional sense.

There is a rough chronology from past to present, and there are all the usual details about his life and career, but in many respects it doesn't obey the rules. There are large parts of the writer and comedian's story that are almost completely missing (there's pretty much nothing about Fawlty Towers, for example) and there are whole sections in which Cleese seems to step out of the pages altogether to analyse what he's just written or is about to write. It's as if he becomes one of the readers rather than the writer and can goggle and gawk and laugh along with us.

All of this experimentation and self-analysis is good for the book, and none of it should be surprising. It's good because it means So, Anyway breaks away from the shallow conventions of the famous person's autobiography. It's unsurprising because Cleese is a comedian who has spent a lot of his adult life in therapy, which means he is highly analytical and critical of his life but also aware that life needs a bit of light relief as well. The result is a book that is frequently hilarious, occasionally lyrical and always thoughtful. It is a fine and funny achievement.

The laugh-out-loud sections are pure farce. Cleese explains, for example, what happened when he tried to learn how to waterski, and there is also a marvellous section in which he relates how, as Lucifer in a production of Doctor Faustus, he tried to convey the purest form of evil while also getting stuck in a curtain. It is silly, chaotic and perfectly timed.

The book also has a delightful rhythm and structure to it, which helps reveal the thoughtful, angry and obsessive elements of the Cleese psyche while never allowing them to become overbearing. At one point, while talking about his time in Cambridge, where he met some of the other Pythons for the first time, he starts to think about what intelligence actually is and explores the American professor of cognition Howard Gardner's theory that there are nine different kinds. "Which helps me understand why I sometimes think I am quite bright and sometimes feel like a complete dolt," says Cleese.

The great achievement of the book is that he keeps all of these elements in perfect balance while keeping to some biographical conventions and breaking others. For example, when he gets to the point in the book where he reproduces some of his more obscure sketches from the 1960s, he has one of those moments where he steps out of the book and comments on what's going on: the fact that he is re-publishing material that is already out there.

"Lazy bastard! I hear you cry," he writes, "But I believe I can justify my behaviour ... The sketches are really funny (in my opinion and it's my f***ing book) ... The fact is that most of you don't give a tinker's cuss for me as a human or feel for the many different forms of suffering that make me so special. No, you are just flipping through my heart-rending life story in the hope of getting a couple of good laughs, aren't you?"

You can imagine Cleese saying all of this, eyes dilating, veins pulsing, and it's one of the more enjoyable and unconventional parts of the book. A more conventional section is the one that relates to his childhood and his over-anxious mother. Possibly, Cleese dwells on this time of his life for the same reason he keeps stopping and analysing pretty much everything: he's had a lot of therapy, and therapists often believe the explanation for behaviour lies in childhood.

What could be annoying and tiresome in some people, isn't in Cleese. And anyway, isn't it good to think about our lives in the way Cleese does? Isn't part of the problem with many memoirs the fact that they are just names and dates and a bit of boasting?

What Cleese does instead of that is stand back and ask questions of himself and others. But he also does something else constantly, which is why this is such a wonderful and inventive book: he throws back his head and laughs.