As a very young man, Muller worked in the workshop of his father who was a lithographer, subsequently studying under K. Blaas. Following this he travelled to Egypt, The Balkans and Turkey, painting Orientalist subjects. Returning home he painted Viennese scenes. His works are best known for their excellent colour and light effects. He became the director of The Academy of Art in Vienna and exhibited in Vienna, Berlin and Dresden. Gratz, Munich and Vienna Museums have conserved his works.