Byggmark grew up in Tärnaby . After gaining racing experience at FIS races from the age of 15 , he started in 2003 for the Swedish national team in the European Cup . There he drew attention to himself in particular in the slalom from December 2005 with top results. In February 2005, he had already made people sit up and take notice at the Junior World Championship in Bardonecchia, Italy, with a sixth place in giant slalom and seventh place in slalom.
He made his debut in the World Cup in January 2005 in Kitzbühel , but initially remained without a place in the top ranks during his sporadic appearances. For the 2006/07 season Byggmark moved up in the Swedish World Cup squad. Right at the start of the season in Levi , Finland , he surprisingly drove to sixth place with the second-best running time in the second run. Three weeks later he confirmed his performance with fifth place in the Beaver Creek slalom .
On January 27, 2007, he won his first World Cup race, the Kitzbühel slalom. Only 24 hours later he was able to confirm this success with the second victory in Kitzbühel. On January 30, 2007 he reached second place in the Schladming night slalom . He finished third in the Slalom World Cup in the 2006/07 season . At the 2007 World Ski Championships in Åre , he won the silver medal in the team competition with the Swedish team . He did not achieve another result after failures in slalom, giant slalom and super combined.
In the 2007/08 season Byggmark reached three second places in the slaloms of Bad Kleinkirchheim , Wengen and Kitzbühel. Otherwise, however, he had to struggle with many failures and he fell back to tenth place in the Slalom World Cup. He also had to accept numerous failures in the 2008/09 season. Byggmark could only score three times and achieved tenth place in the slalom of Alta Badia as the best result . Even at the 2009 World Championships in Val-d'Isère , he did not reach the finish line in either slalom or giant slalom. Due to the lack of success in the World Cup, he started again increasingly in the European Cup from February 2009.
In the 2009/10 season Byggmark again only reached the goal in three World Cup slaloms. His best result was 13th place in Alta Badia . He took part in the 2010 Winter Olympics in Vancouver and finished in 22nd place. In the European Cup he won the slalom in Pozza di Fassa this winter and achieved third place in the slalom classification with another podium. In the 2010/11 season Byggmark also improved significantly in the World Cup. He was very consistent and scored points in nine of the ten World Cup slaloms that winter. For the first time in more than two years, he again achieved top 10 placements. At the Alpine World Ski Championships 2011 in Garmisch-Partenkirchen , he surprisingly won the silver medal. In the 2011/12 World Cup season, he achieved six top 10 placements.
As third in the Levi slalom on November 11, 2012, Byggmark was back on the podium in a World Cup race after more than four and a half years. At the 2013 World Cup , he won the silver medal in the team competition. During summer training in Saas-Fee he suffered a cruciate ligament rupture in September 2013 , which meant that he missed the entire 2013/14 season. In the following winter of 2014/15 he achieved another remarkable result with third place in the slalom in Madonna di Campiglio , as well as in winter 2015/16 with fourth place in the slalom in Wengen. On the other hand, he could only show one countable result in winter 2016/17. Recurring knee problems caused him to end the season in January 2017. Finally, Byggmark announced his retirement as a top athlete on April 6, 2017.