Elektra The BBC Promenade Concerts season opens with a performance of Richard Strauss 's dramatic one-act opera live from the Royal Albert Hall in London. Andrew Davis , Chief Conductor of the BBC Symphony Orchestra, conducts this horrific story of obsession, murder and revenge in ancient Greece. Davis says: "The Proms always end with Land of Hope and Glory, but this year we begin by entering a land of despair and gore through Richard Strauss 's inimitable adaptation of Greek tragedy. One hundred continuous minutes of the composer at his most powerful - sung by an exceptionally strong cast - should ensure a chilling and thrilling start to this great festival." Introduced by James Naughtie.

Tonight's Prom marks anniversaries of two popular nationalist composers - Grieg and Tchaikovsky - but begins with Stravinsky's scintillating ballet-score Petrushka, in the original 1911 version. During the interval, there is a visit to Bergen to sample some of the novel ways in which Norway is celebrating Grieg's life and work. Part 2 comprises four songs by Grieg and the concert ends with Tchaikovsky's Suite No 3. The BBC Symphony Orchestra is conducted by Alexander Lazarev, and the soloist in the Grieg songs is the Finnish soprano, Karita Mattila, winner of the 1983 Cardiff Singer of the World Competition. "They represent the typical Grieg style, very romantic, very melodic, with lovely phrasing - a treat for a singer," she says. "They are quite intimate pieces, reflective rather than bravura. I love them and I'm very proud to sing them at the Proms." James Naughtie introduces the concert.

A feast of baroque music is performed by the Virtuosi di Roma, one of the world's most celebrated chamber orchestras. They play without a conductor and in tonight's concert offer five concertos, including Boccherini's most famous cello concerto. Introduced by James Naughtie from the Royal Albert Hall.

Claudio Abbado conducts tonight's Prom featuring the Gustav Mahler Youth Orchestra, which draws its players from all over the world and which Abbado helped to create. The concert begins with the dramatic Songs and Dances of Death by Musorgsky, featuring the Russian baritone Dmitri Hvorostovsky who won the Cardiff Singer of the World Competition in 1989. He says: "I am very excited to be making my Proms debut and to be working with one of the world's greatest maestros, Abbado, for the first time and with such an exciting youth orchestra with players from many Eastern European countries. And I'm proud to be singing one of the strongest song-cycles in the Russian repertoire." Part 2 is Anton Bruckner's monumental Fifth Symphony. During the interval, there is a look behind the scenes with the orchestra on its summer course in Bolzano, northern Italy, as Abbado prepares the young players for the Prom. Introduced by Michael Berkeley.

The brilliant young American trumpeter Wynton Marsalis plays with his septet, a line-up of internationally acclaimed jazz musicians, for this late-night Prom live from the Royal Albert Hall, London. Marsalis says, "The Proms are renowned for an audience of all ages - and that's for me. I don't believe in this endless celebration of youth. I love young people - but I love old people, too. And middle-aged people! It's the flow of life that's important. Jazz is what I was put on this earth to play and my music is for everybody." Born in 1961, Marsalis entered the Juilliard School at the age of 18 and was soon playing on Broadway and with the Brooklyn Philharmonic. He describes himself as a jazz musician who can play classical music, and in 1984 he simultaneously carried off recording awards for best jazz soloist and best classical soloist with orchestra.

The Oslo Philharmonic under its conductor Mariss Jansons is now one of Europe's top orchestras. Their concert tonight from London's Royal Albert Hall begins with a bizarre work by Russian composer Alfred Schnittke. He calls it (Not) a Midsummer Night's Dream and in it a tune which could be by Schubert is taken on a nightmarish journey. Schnittke says of this tune: "I didn't borrow it, I faked it!"

An entertaining programme aimed at a younger audience is provided by this afternoon's concert, of which BBC1 is transmitting the first half live. Raymond Leppard conducts the BBC Symphony Orchestra in Britten's ever-popular The Young Person Guide to the Orchestra, followed by Dohnanyi's charming Variations on a Nursery Song. David Owen Norris , piano soloist in the Dohnanyi, comments: "I like musical jokes and this one, like all the best jokes, should not be given away. There can be nothing more important than a concert designed for a younger audience. My children - Barnaby, 6, and Josiah, 4 - will be there to share it. And the joke." Introduced by James Naughtie from the Royal Albert Hall in London.

Simon Rattle conducts two ensembles with which he is particularly associated - the City of Birmingham Symphony Orchestra and the Birmingham Contemporary Music Group. To begin, the latter make their Proms debut in a performance of Schoenberg's early and ebullient Chamber Symphony No 1. Then the Italian pianist Maurizio Pollini, making his first television appearance at the Proms, joins the CBSO for Mozart's Concerto No 24, K491. After the interval Rattle conducts the orchestra in Stravinsky's ballet Pulcinella, a witty pastiche based mainly on themes by the 18th-century Neapolitan composer Pergolesi.

Always a very British affair, the traditional final concert of this year's BBC Proms returns to an all-British programme. This first half opens with Holst's ballet music from A Perfect Fool, followed by Arnold's Clarinet Concerto No 2 (the soloist is Michael Collins ). After shorter pieces by Delius and Lord Berners, part 1 ends with Lambert's Rio Grande, which brings together mezzosoprano Delia Jones , pianist Kathryn Stott , the BBC Singers and BBC Symphony Chorus. Barry Wordsworth conducts the BBC Symphony Orchestra, and the concert is introduced from the Royal Albert Hall by Richard Baker.

Highlights of the summer Proms. The BBC Symphony Orchestra under conductor Raymond Leppard plays Tchaikovsky's Symphony No 2, (Little Russian) and Ravel's Sheherazadewith soprano Judith Howarth.