After a couple of fairly lean years for people who enjoy giving the gift of music for the holidays, the new century has begun with a bumper crop of boxed sets to consider for gift lists. Jazz is especially well represented among this year''s multi-CD sets, with sets from three of the true giants of the genre--Duke Ellington, Miles Davis and Louis Armstrong. But there are quality choices for virtually every genre of contemporary music. Here is a look at some suggestions for music gift giving.

Various Artists:

Ken Burns Jazz: The Story Of America''s Music (Columbia Legacy)

This five-CD set is the soundtrack to Burns'' forthcoming PBS series on the history of jazz, and as such promises to provide a wide-ranging overview of the genre''s development. It''s a goal the set only partially achieves. Focusing strongly on Louis Armstrong, Duke Ellington, Billie Holiday, the set is weighted too strongly toward pre-1960 recordings--highly influential artists such as Miles Davis, Charles Mingus, John Coltrane and Wynton Marsalis get only a cursory look in the set. The inference, of course, is that jazz faded markedly by the 1960s, an argument that has merit. But this keeps the set from providing the balance its subject deserves. Still, the five discs are filled with wonderful music. And for those who want an introduction to the jazz genre, Ken Burns Jazz is a fine place to start.

Duke Ellington:

The Duke: The Essential Collection, 1927-1962 (Columbia Legacy)

To many jazz fans, Ellington is the single greatest figure in the history of jazz, and this three-CD overview collects 65 of his greatest and most popular songs.The tracks have been wonderfully remastered, making this the best sounding Ellington collection I''ve heard. Of course, Ellington also recorded for MCA and RCA Records during his long and illustrious career, with his recordings in the early 1940s with RCA being an especially impor- tant period. Those performances aren''t represented here. But this is an outstanding collection that captures the breadth and sheer greatness of much of Ellington''s landmark career.

Miles Davis & John Coltrane:

The Complete Columbia Recordings, 1955-1961 (Columbia Legacy)

The latest in an ongoing series of boxed sets devoted to specific periods of Davis'' groundbreaking career, this six-CD collection documents perhaps the peak era of the trumpeter''s career. (Pivotal albums such as Kind Of Blue and Round About Midnight were recording during this time.) While the set is centered around the years in which Coltrane played tenor saxophone in a variety of Davis'' lineups, this also means some of the contributions of such stalwarts as pianist Gil Evans, alto saxophonist Cannonball Adderly, and pianist Red Garland are also represented. The set, which comes with many unissued alternate tracks, is a stunning document of the period where Davis experimented liberally and developed the modal style that would define his sound for years to come--and rewrite the rules of jazz for generations to follow.

Louis Armstrong:

The Complete Hot Five And Hot Seven Recordings (Columbia Legacy)

It''s

said that Armstrong invented jazz as we know it, creating a solo voice for the cornet and a rhythmic blueprint that would serve as the basis for the genre for decades to come. No argument there. And the music that laid the groundwork for Armstrong''s career--and jazz in general--is collected on this outstanding four-disc set. In fact, many Armstrong enthusiasts consider the music he recorded with his Hot Five quintet and the augmented Hot Seven lineup between 1925 and 1929 to be the finest music in his long career. Listening to these spirited, innovative and entertaining sides, it''s hard to dispute that point either. The songs in this collection have been available on various compilations, but never collected in their entirety in a single set. Historically accurate, comprehensive and carefully remastered, The Complete Hot Five And Hot Seven Recordings stands as one of the most important documents of jazz.

Los Lobos:

El Cancionero: Mas Y Mas (Warner/Rhino Archives)

For my money, Los Lobos is the best rock band on the planet today. Even if one doesn''t share that opinion, this four-CD anthology should provide convincing proof that few groups are better. Covering the Mexican-American band''s entire 23-year career, this set traces the band from the rousing bluesy rock of their early CDs through the more experimental material of recent CDs that has found Los Lobos rewriting the rules of roots rock, filling their songs with inventive arrangements, surprising sonics and first-rate songcraft. Along with most of the band''s best album tracks, this collection also includes worthy tunes that appeared on soundtracks and tribute albums, plus a sampling of music from the band members'' various side projects. Well suited to both the casual fan and those who are fairly familiar with Los Lobos, this is a fine document of a group that two decades into their career is making some of the most exciting and innovative music in rock history.

Jimi Hendrix:

The Jimi Hendrix Experience (MCA Records)

No rock artist has seen his career more thoroughly docu- mented than Hendrix, whose entire recording career spanned less than four years. His four studio CDs have been reissued with bonus tracks; many posthumously released albums have raided the vaults; Nnumerous official concert recordings exist. So it''s nothing short of amazing to hear the four CDs in this set trace Hendrix''s incredible career largely through unreleased performances. With dozens of alternate studio and concert recordings, this set works as something of a hybrid of the Beatles'' "Anthology" series and a live retrospective. The Jimi Hendrix Experience doesn''t replace or surpass the actual studio albums the guitarist recorded, but surprising and impressive performances abound (check out the unissued takes of "Bold As Love" or "Little Wing"). In short, this is a fascinating and highly entertaining look at an artist whose music continues to resound as strongly today as it did 30 years ago.

Stevie Ray Vaughan And Double Trouble:

SRV (Epic/Legacy Records)

Speaking of artists whose music has been exhaustively documented, this three-CD set still manages to find its share of previously unavailable treasures. Though some album cuts are included, the bulk of SRV is devoted to unreleased live versions of Vaughan originals, radio performances and studio outtakes. The live tracks are uniformly inspired and include some choice covers (such as Vaughan joined by Jeff Beck for a tumultuous take of "Goin'' Down" and "Rude Mood/Pipeline," on which Vaughan and his brother, Jimmie, trade licks sharing the same double-neck guitar). The studio outtakes are spottier, but still have some notable moments. New fans will want to own Vaughan''s studio CDs first, but for die-hard fans, SRV will be an essential addition to the Vaughan catalog.

Little Feat:

Hotcakes & Outtakes (Warner/Rhino Archives)

Little

Feat have never achieved major stardom, but at their best (on tunes like "Oh Atlanta," "Fat Man In The Bathtub" and "Dixie Chicken") they created a funky, boogying concoction that was impossible to resist. Two discs of this four-CD set collect the best material the group recorded when the late Lowell George fronted the band. A third disc documents the music the reformed (and still ongoing) band made after 1988 (including winning tunes like "Let It Roll" and "Shake Me Up"). The fourth disc features 25 outtakes, many of which are of somewhat dubious quality. That said, Hotcakes & Outtakes still stands as an overdue tribute to a highly underrated band.

Sam Cooke:

The Man Who Invented Soul (RCA Records)

This four-CD set''s title might be a slight overstatement, yet there''s no denying the profound influence Cooke had on soul and pop music. This comprehensive four-CD anthology show- cases Cooke, one of music''s all-time great vocalists, from his breakthrough 1957 hit, "You Send Me," through his final recordings in 1963. It goes far beyond any previous collection in documenting Cooke''s career and provides ample evidence of his mastery of soul, gospel, pop and blues.

Other Good Choices:

A pair of three-disc sets merit a mention. Johnny Cash''s Love God Murder (Columbia/Legacy) is a themed set that nicely documents the talent and thematic contradictions and complexities of this country legend''s music. The Electric Light Orchestra''s Flashback (Epic/Legacy) features nearly all of the best material from this band, who merged pop with elements of classical music.

There are also a number of single or double-disc collections that provide solid career overviews of a variety of notable artists. These include Soul Asylum''s Black Gold; Cheap Trick''s Authorized Greatest Hits; Ian Hunter''s Once Bitten Twice Shy; Cracker''s Garage D''Or; Lenny Kravitz''s Greatest Hits; Laura Nyro''s Essential Masters; The Kinks'' Come Dancing: The Best Of The Kinks, 1977-1986; Blur: The Best Of Blur; The Psychedelic Furs: Greatest Hits; and James Taylor''s Greatest Hits Vol. 2.

Borders Books, Sand City, provided CDs for photographic purposes