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, Schrödinger 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.