  Nonlinear magnonics studies the nonlinear interaction between magnons and
other physical platforms (phonon, photon, qubit, spin texture) to generate
novel magnon states for information processing. In this tutorial, we first
introduce the nonlinear interactions of magnons in pure magnetic systems and
hybrid magnon-phonon and magnon-photon systems. Then we show how these
nonlinear interactions can generate exotic magnonic phenomena. In the classical
regime, we will cover the parametric excitation of magnons, bistability and
multistability, and the magnonic frequency comb. In the quantum regime, we will
discuss the single magnon state, Schr\"{o}dinger cat state and the entanglement
and quantum steering among magnons, photons and phonons. The applications of
the hybrid magnonics systems in quantum transducer and sensing will also be
presented. Finally, we outlook the future development direction of nonlinear
magnonics.
