Gunnar H. Jónsson was his first teacher. From 1976 to 1978, he studied at Reykjavik Music School. Then, from 1984 – 1986, he was at Berklee College of Music in Boston. He started playing with bands when he was young, and people immediately responded enthusiastically to his music, for example, with the bands Rifsber and Brunalidid. However, he was best known for his playing with Studmenn, which most countrymen call the band for all Icelanders. He was one of the founders of Thursaflokkurinn. This band’s catchy original arrangements revitalised respect for Icelandic folksongs. The band released records that the nation will be listening to for generations to come. Through the years, Thórður has been an extremely popular session player and has played backing tracks on many performing artists’ records. In addition, he has worked for television and theatre. He has also taught at the Hafnarfjörður Music School, the Association of Icelandic Musicians’ Music School, and the Advanced Icelandic Music School.