This primer is the most unintimidating teacher of Fortran around. It is designed to teach complete novices to communicate with the most sophisticated computer systems. It was written for people who could make direct use of the computer's skills but who themselves know nothing of computers and little enough math beyond that needed to define particular problems. It will teach them, bit by bit, to read and write Fortran IV, a succinct and powerful general-purpose computer language but one especially useful for solving scientific and mathematical problems. The emphasis throughout is on programs that are prepared and tested by means of on-line interactions between user and computer. In the already visible future, the author observes, practically all computer users whose main professional interest is outside programming as such will make exclusive use of this mode. (In the interim, to cover computer installations that are off-line, the book also takes note of the technique of batch processing.) From the start, each chapter presents and explains an actual program, ranging from short and primitive to full-size and complex. In fact, the greater part of the text introduces various delimited concepts and methods by means of showing how they are embedded in programs that in themselves solve real and interesting problems. Thus, for example, subroutines first appear in a program that makes computations based on the progress of a 1000-step random walk; logical variables are defined in connection with a program that solves a chess problem; block data and run-time considerations are taken up with an orbiting planet program; and 2-D arrays are introduced in the exposition of a spiral-drawing program. The book is formatted as a computer print-out. And part of the book was actually written by the computer, in the sense that what the computer printed out in executing the programs assigned to it is directly reproduced. Moreover, the book itself operates something like a program on the student. Quizzes at various points loop him back to previous sections if his answers do not match those given or, if it seems appropriate, the student may be directed to skip over certain expository sections and advance to new material. The text is developed in such a way that it is not necessary for the student to have access to an on-line terminal. However, if he does, he will be able to progress in skill and confidence even more rapidly.