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Their Greatest Hits (1971–1975) is a singles compilation album by the American rock band the Eagles, released in 1976. As of November 2009, 29 million copies have been shipped in the domestic market, making it tied with Michael Jackson’sThriller as the best-selling album in the United States. With an additional 13 million internationally, for a total of 42 million, it is one of the top-selling albums in music history.

Their Greatest Hits (1971–1975) comprises nine best-selling singles released between 1972 and 1975, as well as “Desperado”, which had never been previously released as an A-side. All single tracks but “Tequila Sunrise” charted in the top 40, with five in the top ten, and “One of These Nights” and “Best of My Love” both topping the singles chart. With such airplay success in the span of a little over four years, the band became a formidable presence on American commercial radio in the 1970s, and Their Greatest Hits (1971–1975) debuted at number four on the Billboard 200 album chart upon its release.

On February 24, 1976, the album achieved the distinction of being the first to receive the RIAA Platinum award,  in recognition of one million shipments in the United States. On November 10, 1999, it became the all-time best-selling album in the United States when it was certified 26× Multi Platinum. It was certified at 29× Multi Platinum on 30 January 2006,  and has sold over 42 million copies worldwide to date.  Michael Jackson’s Thriller is the only other album certified 29× Multi Platinum. Their Greatest Hits (1971–1975) is listed at #1 on the RIAA’s “Top 100 Albums”.

Track listing

Side One

Take It Easy – Eagles

Witchy Woman – Eagles

Lyin Eyes – One of These Nights

Already Gone – On the Border

Desperado – Desperado

Side Two

One of These Nights – One of These Nights

Tequila Sunrise – Desperado

Take It to the Limit – One of These Nights

Peaceful Easy Feeling – Eagles

Best of My Love – On the Border