  In the current book I suggest an off-road path to the subject of optimal
transport. I tried to avoid prior knowledge of analysis, PDE theory and
functional analysis, as much as possible. Thus I concentrate on discrete and
semi-discrete cases, and always assume compactness for the underlying spaces.
However, some fundamental knowledge of measure theory and convexity is
unavoidable. In order to make it as self-contained as possible I included an
appendix with some basic definitions and results. I believe that any graduate
student in mathematics, as well as advanced undergraduate students, can read
and understand this book. Some chapters (in particular in Parts II\&III ) can
also be interesting for experts. Starting with the the most fundamental, fully
discrete problem I attempted to place optimal transport as a particular case of
the celebrated stable marriage problem. From there we proceed to the partition
problem, which can be formulated as a transport from a continuous space to a
discrete one. Applications to information theory and game theory (cooperative
and non-cooperative) are introduced as well.
  Finally, the general case of transport between two compact measure spaces is
introduced as a coupling between two semi-discrete transports.
