In his book-laden West Hampstead flat, Steven Isserlis seems both touched and proud to see his own name on a slim new volume alongside that of his musical hero, Robert Schumann. He has "revisited" the composer's book of advice to young musicians, updating the language a little and adding thoughts of his own to explore and amplify the originals; the result has just been published by Faber & Faber.

Isserlis has a special bent for communication, both on the cello and on paper. He has previously written two children's books about composers, and it's likely that the Schumann project will not be the last. In its sequence of aphorisms - soundbites, perhaps, but ones of real substance - Isserlis's text accompanying Schumann's offers a special blend of clear thinking, artistic rigour and off-the-wall humour fed by the influence of Monty Python and the Marx Brothers. "I love Harpo Marx - I made a radio programme about him, called Finding Harpo's Voice," Isserlis remarks.

But why the devotion to Schumann in particular? "I find his music wondrous. All of it," says Isserlis. "But I also love his character. Once, as a child waiting for a cello lesson, I picked this slim red book, Letters of Robert Schumann, off the shelf and began to read. And I thought: what a wonderful way to write; what a wonderful man. I re-read them recently. He's just a good, kind, generous, noble person."

Schumann, born in the German town of Zwickau in 1810, married the love of his life, the pianist Clara Wieck, in 1840; the couple had eight children. Perhaps it is no wonder that works such as his Album for the Young are so full of tenderness. His advice, intended for an audience of budding composers and instrumentalists, but also fascinating for the general music-loving public, focuses on developing a healthy attitude towards music and the study of it, an outlook Isserlis shares:

"Schumann says, for example, that there is no contradiction between thinking and feeling. People sometimes seem to think that if you analyse a piece of music you can't be emotional about it. That's rubbish. "If you analyse a piece, you're learning the story of that piece, and that's what makes you emotional."

And Schumann, too, has a fine sense of humour: "You can learn quite a lot from singers, but do not believe all that they say," he writes.

Schumann's generosity and kindness have been somewhat overshadowed in the past by people's fascination with his mental instability. "It sounds very much as if he was manic depressive," Isserlis reflects, "and probably syphilitic as well. It's not a great combination."

But that does not affect the quality of his musical thinking: "Someone asked me on which points I disagree with Schumann. And I don't. I can't imagine disagreeing with Schumann. You can't disagree with his pieces. They are what they are. Schumann. Sacred."

If Isserlis's response to Schumann's words is heartfelt, so is his playing of the music. His latest CD, in which he is joined by the violinist and conductor Joshua Bell, the Academy of St Martin-in-the-Fields and pianist Jeremy Denk, features a rare arrangement of the Schumann Violin Concerto's slow movement alongside the Brahms Double Concerto for violin, cello and orchestra, and the original version of Brahms's Piano Trio No.1 in B major (the disc is called For the Love of Brahms). The trio is full of musical quotations and implied messages, written after the young Brahms first met Robert and Clara Schumann via the violinist Joseph Joachim.

In the more famous, revised version, Brahms excised most of the personal element - which makes the original all the more fascinating.

The Double Concerto, a much later work, was written as a gesture of reconciliation after Brahms's long friendship with Joachim ruptured - and it worked. "The piece is about friendship, as much as any piece of music can be," Isserlis says. It's also a gesture of friendship for Isserlis: Bell has been a particularly close friend and colleague for nearly 30 years.

"Josh is like my younger brother," says Isserlis. "It reminds me of that Marx Brothers film Go West when someone asks Chico, 'Do you love your brother?' And he says, 'Nah, I'm just used to him'. We're very used to each other! Whenever we meet, we just pick up where we left off."

The fellow feeling, he adds, may be partly to do with their shared Jewish heritage: "I'm great friends with lots of musicians who are not Jewish but it could be that, with Josh, there's an extra bond."

If anything, he adds, they have grown closer in musical terms recently. "Because of Josh's association with the Academy of St Martin-in-the-Fields [Bell is its music director] he has been doing much more repertoire such as Beethoven symphonies. At one point he was doing quite a bit of crossover."

Isserlis, though, has rarely ventured into that territory. "I can't play American folk music, tango, things like that. I couldn't do it well, so I wouldn't do it at all," he says. "Pop is OK - I've played on a friend's album or two as a favour, just for fun - but I prefer to stick to what I try to do well."

The Schumann Violin Concerto's slow movement involves a crucial cello solo, and Isserlis has run to earth a version by no less a personage than Benjamin Britten: an arrangement for string orchestra including a new coda to round off the piece (the original segues into the last movement). He spotted it in the catalogue of the Britten-Pears Library and was curious: "It was written for a concert in Aldeburgh in memory of the horn player Dennis Brain on 19 June 1958 - six months to the day before I was born."

The family tree in which he arrived that December contains remarkable names: Moses Isserles, the 16th-century rabbi of Krakow, plus Felix Mendelssohn, Helena Rubinstein and Karl Marx ("I think he's my ninth cousin five times removed…").

Steven's grandfather, Julius Isserlis, was a distinguished composer, born in Russia and educated at the Moscow Conservatoire. In the 1920s, he took the opportunity to join a delegation of Russian musicians heading for the West on a propaganda exercise, did not return and settled with his family in Vienna.

Isserlis's father, George (who died just short of his 95th birthday in 2012), recalled that, when they were looking for lodgings, an elderly landlady refused to accept them upon hearing Julius was a musician: her aunt, she'd recounted, had once had a terrible lodger who was a musician, shouted at everybody and spat on the floor. His name was Beethoven.

George, a metallurgist and keen amateur violinist, grew up surrounded by Vienna's rich ferment of artistic activity. But when the Nazis seized power in 1938, the family was fortunate to escape to Britain. Here, George was interned for a short time on the Isle of Man, where he became friendly with members of the future Amadeus Quartet and played duos with its leader-to-be, Norbert Brainin.

The influence of this heritage and of his main cello teacher, Jane Cowan, helped to instil in Isserlis the uncompromising but always humane passion for musical communication that he passes on today in playing, writing and teaching.

Not least, he is director of the International Musicians Seminar, Prussia Cove, Cornwall, a course attended by the crème-de-la-crème of teachers and students. His life has by no means been plain sailing - his partner of 28 years, Pauline, died of cancer in 2010 - but music, as he has often said, has provided an essential support and outlet.

The question remains whether today's younger generation can share the attitude that music is something sacred, as he and Schumann both advocate. "It's not a sport," Isserlis declares. "I say it in the book and I've said it many times: music is not a sport and it should be taught as a mixture of religion and science. You find out as much as you possibly can about it and approach it with respect. You don't make it a vehicle for impressing people and showing off.

"Actually I think the new generation has this outlook still more, at least among violinists and cellists," he adds. "They really respect the music. I think we went through a bad phase about 20-30 years ago. But those in their late teens and early twenties today seem to have a much better attitude and are emerging much more rounded as musicians."

Isserlis has a busy autumn. You can hear him in a Wigmore Hall BBC Lunchtime Concert with the Finnish pianist and composer Olli Mustonen, playing Schumann, Prokofiev and a Schumann-influenced work by Mustonen himself; in December he appears with the London Philharmonic Orchestra to play the Prokofiev Cello Concerto; and he is recording another CD, this time of works written at the time of the First World War, including sonatas by Debussy, Fauré and Frank Bridge, with the pianist Connie Shih.

But alongside his own masterly playing, perhaps the Schumann-plus-Isserlis book of advice can help to spread his musical ideals still further.

"I hope so," remarks Isserlis. "It's been a labour of love."

Robert Schumann's 'Advice to Young Musicians', Revisited by Steven Isserlis, is published by Faber & Faber.

Steven Isserlis plays at the Wigmore Hall, October 3, and the Royal Festival Hall, December 7. 'For the Love of Brahms' is released on Sony Classical