The greatest classical music festival in the world gets underway from the Royal Albert Hall. Katie Derham introduces music on a sea-inspired theme by English composers Vaughan Williams and Britten and two sets of the well-known Paganini variations by Rachmaninov and Polish composer Lutoslawski. There is also the world premiere of Julian Anderson's Harmony. Sakari Oramo conducts the BBC Symphony Orchestra, BBC Symphony Chorus and the BBC Proms Youth Choir and soloists Stephen Hough (piano), Sally Mathews (soprano) and Roderick Williams (baritone).

From the Royal Albert Hall, the Bamberg Symphony Orchestra conducted by Jonathan Nott perform Mahler's Fifth Symphony, opening a Thursday night season featuring Orchestras of the World at the BBC Proms. Katie Derham introduces this popular work by Mahler with its intensely lyrical fourth movement, the Adagietto, written as a love letter to the composer's young wife Alma and later made famous when featured in the film Death in Venice.

From the Royal Albert Hall, Samira Ahmed introduces the BBC Philharmonic Orchestra conducted by Juanjo Mena, who perform Rachmaninov's Piano Concerto No 2 and Nielsen's Fourth Symphony. The piano soloist is the extraordinary young Japanese pianist Nobuyuki Tsujii, whose blindness is no barrier to his musical talent. Nielsen's Fourth Symphony, 'The Inextinguishable', features a battle between two sets of timpani.

A rare opportunity to hear the Orchestra of the Academy of Santa Cecilia, Rome conducted by Sir Antonio Pappano at the Royal Albert Hall. The Prom begins with a classical gem, Mozart's Haffner Symphony, and ends with the melancholy and high drama of Rachmaninov's Second Symphony. 18-year-old Canadian piano phenomenon Jan Lisiecki makes his Proms debut as the soloist in Schumann's Piano Concerto.

The newly-formed National Youth Orchestra of the USA comes to the Proms under the conductor Valery Gergiev, performing Tchaikovsky's Violin Concerto with Proms favourite Joshua Bell as soloist and Shostakovich's 10th Symphony, a stirring and powerful musical protest against oppression.

Leading British composer Thomas Adès joins presenter Tom Service to reflect on his new work Totentanz, or Dance of Death, which receives its world premiere at the Royal Albert Hall. Adès himself conducts the BBC Symphony Orchestra in a programme which also features Benjamin Britten's Sinfonia da Requiem and Polish composer Witold Lutoslawski's Cello Concerto with soloist Paul Watkins.

From the Royal Albert Hall, Katie Derham introduces the Mahler Chamber Orchestra, a truly international orchestra whose players come from 20 different countries. Formed in 1997 it has rapidly established a reputation as one of Europe's best ensembles. Under conductor Daniel Harding it plays symphonies by Schumann and Sibelius and is joined by the Liverpool-born pianist Paul Lewis for a performance of Mozart's Piano Concerto no 25.

A Prom concert of music and dance introduced by Samira Ahmed from the Royal Albert Hall. The Antonio Marquez Company from Spain joins the BBC Philharmonic Orchestra to dance in Ravel's Bolero and Falla's Three-Cornered Hat. Before that, Juanjo Mena conducts a performance of Beethoven's 7th Symphony, described famously by Wagner as 'the apotheosis of the dance'.

The Sunday series at the Proms continues with an all-Russian programme of Prokofiev and Shostakovich, performed by Danish conductor Thomas Sondergard with the BBC National Orchestra of Wales at the Royal Albert Hall. Tom Service presents his distinctive take on the music, featuring soloist Daniel Hope in Prokofiev's Violin Concerto No 2 in G minor, followed by Shostakovich's mighty Symphony No 11, The Year 1905.

The Bavarian Radio Symphony Orchestra conducted by Mariss Jansons performs Piano Concerto No 4 by Beethoven (soloist Mitsuko Uchida) and Symphonie Fantastique by Berlioz.

Beethoven's 5th Symphony headlines this Prom, the most iconic symphony in western music with its dramatic opening 'fate' motif. The symphony is preceded by Beethoven's Coriolan Overture, a work of contained ferocity. In contrast the concert opens with Strauss's Blue Danube Waltz, the ultimate expression of the pleasures of Viennese high society. Donald Runnicles conducts the BBC Scottish Symphony Orchestra. Introduced from the Royal Albert Hall by Suzy Klein.

Sarah-Jane Crawford and Charlie Sloth present the first ever Urban Prom from the Royal Albert Hall. A selection of artists sing and rap their biggest hits - including gospel singer Laura Mvula, hip-hop star Wretch 32, rapper/producer/DJ/songwriter Fazer, old-school soul rapper Maverick Sabre, soul singing maverick Jacob Banks and UK grime scene sensation Lady Leshurr rapping with Labrinth - all performing alongside the BBC Symphony Orchestra. The euphoric musical experience is led by conductor and arranger Jules Buckley, who has created a unique, unforgettable Prom.

From the Royal Albert Hall, the Santa Cecilia Orchestra and Chorus, based in Rome and conducted by Sir Antonio Pappano, bring an authentically Italian touch to a celebration of the 200th anniversary of Verdi's birth. In a concert featuring his religious works, Italian soprano Maria Agresta makes her Proms debut singing rarely performed settings of Ave Maria and Libera Me. The Prom concludes with Verdi's final work, Four Sacred Pieces, completed a few years before his death in 1901.

Sir John Eliot Gardiner, one of the pre-eminent exponents of the music of JS Bach, returns to the Proms with the Monteverdi Choir and English Baroque Soloists in two profoundly moving works based on events in the life of Christ, the Easter Oratorio and the Ascension Oratorio. Introduced by Suzy Klein.

Brand new sounds from the Proms in Tom Service's modern music series. Tom is joined by Southbank classical music supremo Gillian Moore to discuss a selection of premieres and new commissions from across the season at the Royal Albert Hall. Music ranges from the world premieres of John McCabe's Joybox and Mark-Anthony Turnage's Frieze to Murray Gold's new composition to mark Doctor Who's 50th birthday.

From the Royal Albert Hall, the Rotterdam Philharmonic Orchestra, under their charismatic French-Canadian conductor Yannick Nezet-Seguin, bring a programme of ill-fated love to the BBC Proms. Tchaikovsky's fantasy overture Romeo and Juliet is followed by Wagner's Wesendonck Leider, a song cycle inspired by the composer's infatuation with the wife of one of his wealthy patrons. Soprano Anna Caterina Antonacci is the soloist. The concert ends with a performance of one of the great orchestral works of the 20th century, Prokofiev's 5th Symphony. Presented by Katie Derham.

At the Royal Albert Hall, Clemency Burton-Hill introduces violinist Nigel Kennedy, who returns to the Proms to give his distinctive version of Vivaldi's Four Seasons, the work he recorded to great acclaim 25 years ago. Joined by the Palestine Strings from the Edward Said Music Conservatory, Kennedy also adds improvisation between each concerto with members of his own Orchestra of Life.

Tom Service presents a thoroughly British edition of his series focusing on 20th century music at the Proms, performed by the London Symphony Orchestra conducted by Daniel Harding. Music includes Michael Tippett's Concerto for Double String Orchestra, Benjamin Britten's Les Illuminations featuring tenor Ian Bostridge, and Elgar's Second Symphony. The concert is dedicated to Sir Colin Davis, president of the London Symphony Orchestra, who died earlier this year.

Celebrating the 50th anniversary of the iconic and much-loved BBC series, this special event at the Royal Albert Hall features Murray Gold's popular music for the show, accompanied by specially edited sequences from the Doctor's most recent adventures. Hosted by the Doctor's friends, Madame Vastra and Strax, the concert also includes a look back at 'classic' Doctor Who series and the music created by the legendary BBC Radiophonic Workshop. Featuring special guest appearances by Matt Smith, Jenna Coleman, Peter Davison and Carole Ann Ford, who played the Doctor's first companion and granddaughter Susan Foreman. Plus, the Doctor and Clara drop in to join in the fun. Performed by the BBC National Orchestra of Wales, the London Philharmonic Choir, with soloists Elin Manahan Thomas, Allan Clayton and Kerry Ingram.

From the Royal Albert Hall, Katie Derham introduces the Gustav Mahler Jurgendorchester, which brings together some of Europe's best young musicians and is one of the most musically exciting and polished youth orchestras in the world. Conducted by Philippe Jordan, the orchestra performs Wagner's Rienzi Overture and Shostakovich's Fifth Symphony and is joined by the flamboyant French pianist Jean-Yves Thibaudet for Ravel's jazz-influenced Piano Concerto in G Major.

At the Royal Albert Hall, Katie Derham introduces the ever-popular John Wilson and his orchestra in a celebration of the music of Hollywood. Bernard Herrmann's Psycho, Erich Korngold's Robin Hood, Max Steiner's Casablanca and Miklos Rozsa's Ben Hur are among the film scores featured, performed by the orchestra Wilson describes as 'a symphony orchestra with an old-fashioned dance band in the middle'. With soloists Venera Gimadieva, Matthew Ford and Jane Monheit. (Prom 59)

As part of the Wagner bicentenary celebrations at the Proms, Tom Service is at the Royal Albert Hall for a concert performance of Wagner's mighty Tristan and Isolde, the opera that marked a defining moment in the evolution of modern music. Semyon Bychkov conducts the BBC Symphony Orchestra and Violeta Urmana and Robert Dean Smith are the lovers for whom the sweet embrace of death beckons. Tom talks to writer and Wagnerite Philip Hensher, while conductor and cast explain the herculean physical and emotional endurance the opera demands of them.

Making their Proms debut, the Orchestra Sinfonica di Milano Guiseppe Verdi are joined by Maltese tenor Joseph Calleja to celebrate the bicentenary of Verdi's birth with a feast of his arias. With their Chinese-American conductor Xian Zhang, the orchestra also take us on a lovelorn trek through the Alps in Tchaikovsky's Manfred Symphony, based on a poem by Lord Byron.

The National Youth Orchestra under conductor Vasily Petrenko are joined by the National Youth Choir, the Irish Youth Chamber Choir, Codetta and a line-up of international soloists to perform Beethoven's Ninth Symphony, the Choral, and new commission Frieze by British composer Mark-Anthony Turnage, based on ideas from the Choral Symphony. Introduced by Simon Russell Beale.

Live from the Royal Albert Hall Katie Derham introduces the final concert of the 2013 Proms season. History is in the making as conductor Marin Alsop takes charge of her first Last Night. Violinist Nigel Kennedy and mezzo-soprano Joyce DiDinato are the star soloists in a programme that includes Vaughan Williams' Lark Ascending and arias by Massenet, Handel and Rossini. The concert begins with a celebratory new piece by composer Anna Clyne and there are works by anniversary composers Wagner and Britten, as well Bernstein's Chichester Psalms for chorus and orchestra.