Alex Welsh was a fine traditional and mainstream trumpeter, who led one of Britain's best jazz groups from the 1950s to the 1980s. Digby Fairweather, who knew him well and inherited Welsh's cornet, joins Alyn Shipton to select the finest available recordings from the Welsh band's long career.

A one-time member of Art Blakey's Jazz Messengers, Cedar Walton is one of the most sought-after and versatile pianists in jazz. He joins Alyn Shipton to discuss records made under his own name, as well as work with Blakey, the Jazztet, Ron Carter and Lee Morgan.

Originally in folk-jazz group Lammas, leader of a regular band at London's Pizza Express and then recruited to join Chick Corea, Tim Garland is now one of Britain's best known jazz saxophonists. In this programme he joins Alyn Shipton to pick not only examples of his work in all those contexts, but also in orchestral settings, with his Lighthouse Trio, Acoustic Triangle, and his current touring band with Americans Joe Locke and Geoff Keezer, known as Storms / Nocturnes.

John Etheridge joins Alyn Shipton to suggest the best recordings by three generations of gypsy guitarists whose work is often overshadowed by Django Reinhardt. Artists covered include the Ferre family, Bireli Lagrene, Fapy Lafertin and the Rosenberg dynasty.

Barbados-born Harry Beckett was one of the most fiery and inventive trumpeters in British jazz, right up until his death in July this year. Chris Batchelor joins Alyn Shipton to look back at Beckett's recordings, and to pick his best performances. As well as a range of music from his own bands, the programme includes Beckett's work with Ian Carr, Mike Westbrook and Graham Collier.

Before his death in 2007, Esbjörn Svensson was regarded as the leading pianist in European jazz. His trio (EST) topped the Swedish charts and appeared on MTV. His appeal was broad enough to reach audiences of every age, and his repertoire stretched from dazzling interpretations of jazz standards by the likes of Thelonious Monk to quirky originals, such as his "Dodge the Dodo" which combined drum 'n' bass ideas with languid jazz balladry. In this programme, John L Walters of the Guardian joins...

Best known as the leader of the fusion bands Tempest and Colosseum, drummer Jon Hiseman's career in jazz covers almost all styles and genres. He talks to Alyn Shipton about a catalogue of recordings that includes free jazz trios with Mike Taylor, big bands, his own groups including Colosseum, and his work with his wife Barbara Thompson in Paraphernalia and the United Jazz and Rock Ensemble.

Phineas Newborn Jr. was one of the finest pianists in jazz history, but his short career was dogged by physical and mental illness and he is now a somewhat obscure figure. In the wake of several recent reissues of Newborn's work, Brian Priestley joins Alyn Shipton to pick the highlights and to reappraise this largely forgotten genius of the piano.

In an archive interview with Alyn Shipton and Geoffrey Smith, the late Johnny Griffin selects his favourite records. The tenor saxophonist was one of the most technically brilliant and audacious soloists in jazz. He died in 2008, but a year or two earlier, he joined Alyn Shipton and Geoffrey Smith in conversation at the Cheltenham Jazz Festival to discuss his personal favourites from his extensive catalogue of recordings.

John Taylor is one of the finest and most influential pianists in British jazz. He joins Alyn Shipton in front of an audience at the 2011 Cheltenham Jazz Festival to discuss his recorded catalogue, including his early collaborations with Kenny Wheeler and Norma Winstone, work with John Surman, and his own trios and duos, including a disc with legendary bassist Charlie Haden.

Bobby Wellins joins Alyn Shipton at the Oxford Jazz Festival to select his key recordings. The Glasgow-born saxophonist achieved stardom for his solo on Starless and Bible Black in Stan Tracey's Under Milk Wood. In conversation with Alyn Shipton at the Oxford Jazz Festival he discusses many other highlights from his recordings.

Composer and saxophonist John Altman joins Alyn Shipton to pick the best records by saxophonist Al Cohn. As well as his solos albums and his lengthy association with fellow tenorist Zoot Sims, the programme covers Cohn's work with Joe Newman and Freddie Green, and as an arranger for Gerry Mulligan's Concert Jazz Band.

Alton Purnell was born on 16 April 1911, and to celebrate his centenary, Mike Pointon joins Alyn Shipton to pick the best records by the New Orleans pianist. The programme covers his work with Bunk Johnson and George Lewis, his own records, and later recordings with Jimmy Archey and with the Legends of Jazz. Both Pointon and Shipton played with Purnell on his UK tours, so this edition of Jazz Library includes some shared insights into his musical world.

Guitarist Mike Stern has been a major figure in jazz fusion throughout his career. In this programme he traces some of his principal associations and picks some of his own best recordings in conversation with Alyn Shipton at the Sage Gateshead, as part of the 2011 Jazz Festival there. The music ranges from his work with Miles Davis and the Brecker Brothers to his long association with saxophonist Bob Berg.

Saxophonist Joe Lovano is one of the most versatile soloists in jazz. In conversation with Alyn Shipton in front of an audience at the 2011 Gateshead International Jazz festival he discusses some of his finest records, from duos with Hank Jones to a range of trios, and from there to octets and his current group Us Five. He also discusses his compositions and work with large ensembles such as his Symphonica project.

A fine saxophonist and a pioneer of jazz flute, James Moody died last December. Alyn Shipton remembers his career and picks his finest records with the help of the man himself in an archive conversation recorded at Ronnie Scott's. He recalls his long association with Dizzy Gillespie and his big hit 'Moody's Mood for Love'.

To celebrate the 92nd birthday of George Avakian, the veteran record producer joins Alyn Shipton to pick his personal favourites from a long career in supervising record sessions, starting in 1939. From the Chicago jazz of Eddie Condon and Jimmy McPartland, the programme covers a vast stylistic range including Erroll Garner, Miles Davis's quintet and his Gil Evans collaborations, the Duke Ellington Orchestra, Dave Brubeck's most famous quartet and the Louis Armstrong All Stars.

On the weekend of what would have been his 80th birthday, the drummer Allan Ganley is heard selecting his favourite recordings in an interview recorded before his death in 2008. He tells Alyn Shipton about his work with John Dankworth, Ronnie Scott and Tubby Hayes, and we also hear Ganley the composer in a variety of settings from trio to big band.

Roy Eldridge, with his fiery tone, brilliant upper register and inventive phrasing, was the most musically combative trumpeter of the swing era. The heir to Louis Armstrong and the main influence on Dizzy Gillespie, his own canon of work stands alongside theirs. New Orleans-born trumpeter Abram Wilson helps Alyn Shipton to select the key recordings by Eldridge, including his creative partnerships with Gene Krupa, Chu Berry, Artie Shaw, Lester Young and Art Tatum.

Dinah Washington was only 39 when she died of an accidental overdose of barbiturates in 1963. Yet in her short life she was one of the most successful of all jazz singers, also crossing into blues and pop territory. Gwyneth Herbert joins Alyn Shipton to pick the essential recordings by Dinah, starting with her bluesy repertoire of the mid-1940s and tracing her career as she became one of the finest interpreters of American popular song. The programme includes her collaborations with Quincy...

Hank Mobley was one of the finest tenor saxophonists in jazz during the 1950s and 1960s. In this programme, fellow saxophonist, author and broadcaster Dave Gelly joins Alyn Shipton to select Mobley's best work. As well as the sessions Mobley led himself, principally for the Blue Note label, the programme looks at his brief period as a member of the Miles Davis quintet.

Killed in a car accident aged just 25, Scott LaFaro was widely regarded as the most technically gifted bassist of the 20th Century. His records with Bill Evans are among the finest jazz trio discs ever made. Bassist Dave Green joins Alyn Shipton to pick the highlights of these, and to trace the other significant records in LaFaro's brief but brilliant career.

Sonny Stitt was one of the finest bebop saxophonists, transferring the style of Charlie Parker to the tenor instrument, as well as developing his own approach to the alto. Fellow saxophonist Alan Barnes joins Alyn Shipton to choose the best examples of Stitt's work, including his recordings with Dizzy Gillespie, Bud Powell and Sonny Rollins as well as the many sessions he led himself.

Ian Smith joins Alyn Shipton to select the best recordings by trumpeter and vocalist Chet Baker, including his early work with Gerry Mulligan, his West Coast quartets and the early collaborations with Art Pepper. There is also a focus on his latterday career, and in particular the records he made in Europe in his final years.

Louis Moholo Moholo arrived in London from South Africa in the 1960s with Chris McGregor's Blue Notes. During his visit to the UK for the 2010 London Jazz Festival, he joins Alyn Shipton to discuss the high points in a long and extensive recording career, that not only encompasses work with fellow South Africans Harry Miller and Dudu Pukwana, but also with mercurial American pianist Cecil Taylor.