To explore, to communicate, to improvise: these are the ideas that propel Italian cellist Giovanni Sollima on a whirlwind of music performance and composition.

Sollima delighted audiences when he last toured with the Australian Chamber Orchestra in 2014 and played at the Four Winds Festival in Bermagui. He now begins his second ACO tour with a concert at Llewellyn Hall on Saturday, June 25. He'll share the stage with two ACO members as soloists, violinist Satu Vanska and double bassist Maxime Bibeau, and the rest of the ensemble in a program that celebrates Italian music, beginning with an arrangement for strings of Claudio Monteverdi's Lamento della ninfa and leading to a performance of Sollima's own composition for cello, strings and continuo, Fecit Neap 17 ...

"When I play concerts I have no time for fear," Sollima says. "I try to be honest and to take care of the communication with the audience."

Another of Sollima's beliefs is that today it is necessary to play all kinds of music

"Once somebody would specialise in early music, or contemporary music or romantic music or rock, but I try to explore everything. And there are so many connections between different styles of music from different times – all the improvisation in both baroque and contemporary music for instance."

He explains that in the last few months he has been playing the viola da gamba again. "I've found it very stimulating and inspiring. We need to know and explore a bit, not just be in one little world. I think it's very healthy to explore all kinds of music."

"With Monteverdi we go back to the first layer of opera. He's such a strong composer and so visionary, modern," Sollima says. "He changed the way of thinking about and making music He was an important bridge between the Renaissance and Early Baroque. You see all the passion and fire inside all his music and the melody is so strong. I think it's good to start the concert with his piece because this is where so much began. He made the DNA of modern music somehow and he introduced new techniques – and not only that; his music has such expressiveness and human feeling."

Vanska and Bibeau will play excerpts from Luciano Berio's Sequenzas for Violin and Double Bass. Berio writes: "To compose Sequenza VIII has been like paying a personal debt to the violin, which to me is one of the most subtle and complex of instruments ... [and it] becomes inevitably a tribute to that musical apex which is the Ciaccona from Johann Sebastian Bach's Partita in D minor, where – historically – past, present and future violin techniques exist."

Berio's Sequenza XIVb is a "reinvention" by Stefano Scodanibbo of Berio's Sequenza IV for cello and uses a diversity of instrumental techniques and exploits the timbral qualities of the double bass.

Vanska will play Paganini's introduction and Variations on Dal tuo stellato soglio from Rossini's opera Moses in Egypt. The fanciful tale goes that in the midst of a recital the strings of Paganini's violin broke, one after the other, until only the G string remained. Undeterred, Paganini improvised, using only the G string. The resulting piece is devilishly difficult with a theme typical of bell canto opera that leads to challenging variations. Bibeau will play Giancinto Scelsi's C'est bien la nuit from Nuits, an abstract bass solo with vibrating low notes.

Another piece in opera style will be Rossini's Une larme, Theme and Variations for Cello and Strings.

"It's a piece like the Paganini that Satu will play," Sollima says, "very sweet, like an opera scena."

Sollima's performance with the Amsterdam Sinfonietta in 2010 can be seen on YouTube and shows his passionate involvement with the music and the manner in which the members of the ensemble revere him.

"Well, it's a magic piece,' Sollima says. 'I just tried to feel that I was a singer of this piece. Sometimes you have to feel that your fingers are like a singer. The piece is full of style – funny, sad, nostalgic,"

Sollima describes Leonardo Leo's Cello Concerto No 3 in D minor as "intense and so dramatic but also very light and fresh. It's elegant. Leo knew how to make the cello sing, cry, scream. It's a great baroque concerto, not often played but really quality music".

Of his own composition, Sollima explains the ellipsis at the end of the title (Fecit Neap 17 ...) means "made in Naples 1700 and something".

"Actually this piece is more connected to the Leo piece – a sort of mirror in the program. I worked on a city project about four years ago with a baroque cello composition that I discovered in Naples. The atmosphere is dark but also dancing. The title comes from the label on a cello by an early cello maker of the time. I wrote a kind of baroque concerto, which is not baroque at all!"

Sollima plays a 1679 Ruggieri cello that his grandmother bought for him.

"I've been playing it for more than 20 years. I sometimes feel that it is sending me a message. In the beginning I felt that this cello was playing me and not me the cello. His name is Francesco – the name of his maker."

Sollima's life, since he was a little child, has been music. He has an incredible overview of music history so what would he choose as a final piece of music to play?

"Well, I'd improvise," he says, "just take the instrument and play what comes out. But, of course, you go to Bach's suite somehow. It's one of the most natural and rich and human pieces of music."