These Lectures on Numerical Analysis are essentially lectures notes of a course on "Advanced Numerical Methods" which the author gave in 1956-57 at the Institute of Mathematical Sciences at New York University. The original notes, prepared by S. d'Ambra and S. Locke, were distributed by the Institute for a number of years in mimeographed form. The author has made extensive revisions in the wording of theorems and proofs and the list of references, but had to refrain from making the major changes that would be required in an attempt to bring the material up to date. It has not always been possible to perfect the informal style of the original notes.It is hoped that even in its present form the book can serve as an introduction to the field for students who have a fair knowledge of linear algebra, of functions of a complex variable, and of the basic facts about ordinary and partial differential equations.