Born in Kranichfeld in Saxe-Weimar-Eisenach, the son of a local medical practitioner, he received his early schooling at the gymnasium of Meiningen, to which place his father had relocated.

After studying natural science at Leipzig as a member of the German Student Corps Thuringia and in various other universities, he engaged as a private tutor, both independently and for families, in the Austrian towns of Graz, Brünn and Trieste.

[1] In Trieste he published an Alpine legend, Zlatorog (1877), and songs of a journeyman apprentice, Lieder eines fahrenden Gesellen (1878), both of which had many editions.

[1] Baumbach was a poet of the informal vagabond school and wrote, in imitation of his more famous compatriot, Joseph Viktor von Scheffel, many drinking songs, among which Die Lindenwirtin ("The Linden Hostess") has endeared him to many German students.

Special mention may be made of Frau Holde (1881), Spielmannslieder (1882), Von der Landstraße (1882), Thüringer Lieder (1891) and his prose, Sommermärchen[2] ("Summer legends", 1881).