  The program of studying general nonlinear Markov processes was put forward in
V. N. Kolokoltsov "Nonlinear Markov Semigroups and Interacting L\'evy Type
Processes" (Journ. Stat. Physics 126:3 (2007), 585-642), and was developed by
the author in monograph "Nonlinear Markov processes and kinetic equations".
Cambridge University Press, 2010, where, in particular, nonlinear L\'evy
processes were introduced.
  The present paper is an invitation to the rapidly developing topic of
noninear Markov processes. We provide a quick (and at the same time more
abstract) introduction to the basic analytical aspects of the theory developed
in Part II of the above mentioned book.
