  Einstein's thesis ``A New Determination of Molecular Dimensions'' was the
second of his five celebrated papers in 1905. Although it is -- thanks to its
widespread practical applications -- the most quoted of his papers, it is less
known than the other four. The main aim of the talk is to show what exactly
Einstein did in his dissertation. As an important application of the
theoretical results for the viscosity and diffusion of solutions, he got (after
eliminating a calculational error) an excellent value for the Avogadro number
from data for sugar dissolved in water. This was in agreement with the value he
and Planck had obtained from the black-body radiation. Two weeks after he
finished the `Doktorarbeit', Einstein submitted his paper on Brownian motion,
in which the diffusion formula of his thesis plays a crucial role.
