Neil Trudinger is recognised as one of the world’s leading authorities on elliptic partial differential equations, his work in this difficult area being noted for its depth and elegant simplicity. He pioneered new test function techniques for obtaining basic estimates for both linear and nonlinear elliptic operators, and is well known for his important work on Orlicz spaces, on the minimal surface equation, and in the theory of fully nonlinear equations. He is the co-author of a definitive monograph on elliptic equations that is the basic reference in the field.