Mumford & Sons released their second studio album Babel on 24 September 2012, with a track listing of 12 songs, and a deluxe edition containing three exclusive songs. The lead single "I Will Wait" premiered on Zane Lowe's BBC Radio 1 show on 7 August. On 29 August 2012, Mumford & Sons recorded their concert at Red Rocks Amphitheatre in Colorado. The Concert was later released on DVD, Vinyl and on iTunes as "Road to Red Rocks". The performance of "I Will Wait" from the concert was released ahead of the DVD on 9 September as the band's official video for the song. On 22 September 2012, the band performed two songs from the new album, "I Will Wait" and "Below My Feet", on Saturday Night Live.  Babel debuted at number one on the UK Albums Chart and the US Billboard 200. It became the fastest selling album of 2012 in the UK, selling over 158,000 copies in its first week, and was the biggest selling debut of any album in 2012 in the US, selling 600,000 in its first week, and over a million worldwide. In December 2012, Winston Marshall told NME that the band was rehearsing and writing for their next album.  The first phase of a 2013 world tour in support of Babel was released in November 2012. Their Gentlemen of the Road tour continued through 2013. After performing two shows on 8 & 9 June 2013 at the Austin360 Amphitheater in Austin, Texas, bassist Ted Dwane checked into a hospital the next day. Surgeons found a blood clot on the surface of his brain and performed surgery to remove it. Heeding medical advice to aid Dwane's recovery, the band cancelled the rest of its Summer Stampede Tour, including performances at the 2013 Bonnaroo Music Festival and returned to the UK. Dwane's surgery was successful, and his recovery was such that the band were able to headline the 2013 Glastonbury Festival on 30 June, with the band receiving acclaim for their performance.  After first including select stopover cities in their 2012 Tour, the band again selected five cities in Canada, the UK and US to host a two-day festival with shows on multiple stages as well as various other activities and performances. The first stopover of the 2013 Gentleman of the Road tour was in Lewes, East Sussex, from 19 to 20 July. Next was Simcoe, Ontario from 23 to 24 August, followed by Troy, Ohio from 30 to 31 August. The band rounded out their tour with stopovers in Guthrie, Oklahoma on 6 and 7 September and finally St. Augustine, Florida on 13 and 14 September. The Vaccines, Edward Sharpe & the Magnetic Zeros, Vampire Weekend, Old Crow Medicine Show, Yacht Club DJs, Alabama Shakes and various other bands also performed at many of the stopovers throughout the tour.  After the end of the Babel tour, Mumford and Sons took a five-month break before returning to the studio in February 2014 to start work on their third album.

Answer this question "What were their music influences?" by extracting the answer from the text above.
After the end of the Babel tour, Mumford and Sons took a five-month break before returning to the studio in February 2014 to start work on their third album.