  Here we provide a complete English translation of Walter Gr\"obli's 1877
Ph.D. Thesis, together with some notes on the process. The work considers the
dynamics of point vortices in a two-dimensional inviscid incompressible fluid
and derives a number of exact solutions in the cases of three, four and $2n$
vortices with certain restriction on the vortices' circulation and the symmetry
of the initial configuration.
