This is a revised and enlarged version of the author's book which received wide acclamations in its earlier three editions. It provides a lucid and in-depth introduction to the programming language Fortran 77 which is widely used by scientists and engineers.The fourth edition is completely revised chapterwise and also minor corrections incorporated. A new standard for Fortran called Fortran 90 was introduced in early 90s and compilers for this version of Fortran were sold in early 1995 by computer vendors. All Fortran 77 programs will run without change with Fortran 90 compilers; however some aspects of Fortran 77 have been declared obsolete and will not run on future Fortran compilers_these are explained in this revised edition. An appendix consolidates these features. Fortran 90 is introduced in a new chapter which summarises all its features.