* University of Graz (Austria): He started his academic career as a professor of mathematical physics at the University of Graz in 1869.
* University of Vienna (Austria): He moved to the University of Vienna in 1873, where he held the position of Professor of Mathematical Physics.
* University of Munich (Germany): In 1890, he accepted a professorship at the University of Munich.
* University of Vienna (Austria): He returned to the University of Vienna in 1894 as a Professor of Theoretical Physics.
* University of Leipzig (Germany): In 1900, he moved to the University of Leipzig to take up the position of Professor of Physics.
* University of Vienna (Austria): Finally, in 1902, he returned to the University of Vienna, where he remained until his death in 1906.
His research on statistical mechanics and the development of Boltzmann's equation, which describes the time evolution of a system of particles, was largely carried out during his time at these institutions.