Tonight the doors open for the biggest classical music festival in the world, the BBC Proms at the Royal Albert Hall. To help you plan your summer visits and listening, theartsdesk's critics gently steer you with their own preferences from the 90 concerts on offer. You can also check the complete list of all Proms on another page.

Getting to Mull is an improbably romantic journey to classical music-making. One can easily understand why Mendelssohn was so affected by his experiences in Scotland – and Mull. On the three-hour train journey from Glasgow one sheds the habits of everyday life: the train winds through thickets of Forestry Commission plantations, which suddenly open out into wild panoramas of mountains and lochs, or a dramatic ruined castle against the skyline.

The weekend of 29 to 31 July will see London's Festival Hall transformed into what the venue describes as a “multi–venue vintage playground”. Vintage, founded by Wayne and Gerardine Hemingway, comes to London for the first time to celebrate the popular culture of Britain’s past. The Festival Hall is a fitting host, as it was constructed for 1951’s Festival of Britain and is, itself, a piece of living history.

“In jazz music you have the freedom, you have the expression. You have the visceral and you have the intellectual. Everything can be expressed through jazz, and is expressed through jazz and through the medium of improvisation. This is the highest form of being able to create music.” Speaking at the opening press conference of this year's Copenhagen Jazz Festival, that definition of jazz from the 80-year-old saxophone colossus Sonny Rollins seems as self-contained and eloquent as any other I've heard.

It’s not often that a venue’s stage door is easier to find than its main entrance, but The Old Vic Tunnels is one such location. For those behind Coming Up Later, however, this is all part of the fun of a three-evening underground festival featuring a rather wonderfully haphazard range of performances. The event is the product of The Old Vic’s outreach programme, Old Vic New Voices, and the funding and artistic crowd-sourcing network IdeasTap.com. Such collaboration resulted in an opportunity few emergent creative directors could ignore: a production team, a budget to play with and three expansive tunnels for those who could imagine how best to use them.

It cannot be easy being a veteran pop star on tour. All you want to do are your lovely new songs and all your fans want to hear are your golden oldies. Two weeks ago Ringo Starr showed that he has clearly got to an age where he has decided to give the fans what they want and last night in a sun-kissed field in Kent three more icons embraced their past and bathed in the golden glow of nostalgia.

In its second year under creative director David Ansen and in its new home at the LA Live complex, the Los Angeles Film Festival seems to have recovered from the slightly rocky start of its downtown debut last year. While one or two of the several hundred volunteers still seemed to be in it for the free T-shirt, most were clearly film enthusiasts themselves, eager to swap tips with patrons about screenings and potential sleeper hits.

The remarkable thing about Caryl Churchill, Max Stafford-Clark has said, is that she is "completely new, every time she comes out of the box". Watching the first act to his revival of her most celebrated work, which Stafford-Clark revisits for Chichester Festival 29 years after he directed its Royal Court premiere, you feel Top Girls isn’t so much being lifted fresh from that box as bursting through the lid.

Thursday 23 June

Haven’t left yet but someone sends me an email saying, "Not going to Glastonbury this year and feeling rather smug about it." What are they feeling smug about? The fact that they’re going to have a forgettable, normal weekend while this extraordinary event is going on? It is, of course, to do with ideas of rain. A lot of the pre-Glastonbury coverage focuses endlessly on rain and mud, as if home comforts are everything. When did comfort become the big cultural draw?

The history of maths and music is the history of early Greek philosophy, medieval astronomy, of the Reformation, the Enlightenment and the two World Wars. While mathematics at its purest may be an abstraction, the quest for its proofs is deeply and definingly human, charged with biological, theological and even political motive. Whether through performance or discussions about music, this year’s Cheltenham Music Festival (which begins this week) explores the mathematical processes that have both shaped and echoed the history of Western Europe and its art, tracing musical development from the polyphonic motets of the 14th and 15th centuries to the Minimalist patternings of Steve Reich.