  These are lecture notes for the mini-course \textit{PDE and hypersurfaces
with prescribed mean curvature} held in Federal University of S\~ao Carlos at
the Workshop on Submanifold Theory and Geometric Analysis, August 05 -- 09,
2019. The aim of these notes is to introduce to the geometers useful tools from
the \textit{Theory of partial differential equations} which are used in order
to obtain hypersurfaces with prescribed mean curvature. For instance, graphs
with prescribed mean curvature can be obtained by solving the Dirichlet problem
for a particular quasilinear elliptic partial differential equation of second
order.
