Márton Braun embarked on his cello journey at the age of five in his hometown, Budapest. At fourteen, he became a student of Márta Agócs in Kecskemét, Hungary. In 2017, he commenced his studies under the tutelage of Katalin Rootering at the prestigious University of Music and Performing Arts Munich. Following the completion of his Bachelor's degree, he pursued his Master's studies under Julian Steckel's guidance. Following a one-year Erasmus program under the mentorship of István Varga at the Liszt Academy in Budapest, he is now returning to Munich to continue his studies with Prof. Steckel.

Márton has garnered numerous accolades, including the first prize at the "Antal Friss" competition, a third prize at the international cello competition in Liezen, and another third prize at the "Talents for Europe" international cello competition in Dolny Kubin. He also earned the first prize at the "Gerhard Vogt" international chamber music competition in Schweinfurt.

During the period of 2018-2019, Márton was a recipient of the esteemed "Deutschlandstipendium" scholarship, and he continues to enjoy the privilege of being a scholarship holder at "Yehudi Menuhin Live Music Now."

Márton has gained valuable chamber music experience through collaborations with renowned artists such as Farkas Gábor and Franz Halász. Since 2019, Márton has also been a founding member of the Tedesco Quintet. They have performed in renowned concert halls such as Blaibach Concert Hall, Instituto Cervantes Munich, and Allerheiligen Hofkirche der Residenz, Munich. In 2020, he recorded Mario Castelnuovo-Tedesco's guitar quintet, a recording later released by NAXOS.

Starting from their debut performance at the Kodály Institute, Kecskemét in 2023, Márton has consistently been collaborating with pianist Anna Tonie Weber.