Abstract: With the experimental realization of Bose-Einstein condensation (BEC) and the fast development of the studies on nonlinear effects in BEC atomic matter waves, a new branch of atom optics，“nonlinear atom optics”，had been formed, and has been obtained a series of significant experimental progresses. In this lecture, the study content of nonlinear atom optics and their experimental results and recent progress are introduced in some detail, which includes atomic solitons, four-wave mixing, slow light group-velocity and superluminal light, superfluid and vortex, Josephson effect and phase-coherent amplification of atomic matter waves, and so on.