This is a collection of Prof L D Faddeev's important lectures, papers and talks. Some of these have not been published before and some have, for the first time, been translated from Russian into English. The topics covered correspond to several distinctive and pioneering contributions of Prof Faddeev to modern mathematical physics: quantization of Yang Mills and Einstein gravitational fields, soliton theory, the many-dimensional inverse problem in potential scattering, the Hamiltonian approach to anomalies, and the theory of quantum integrable models. There are also two papers on more general aspects of the interrelations between physics and mathematics as well as an autobiographical essay.