This manual contains documentation for users of the NCAR Scientific Subroutine Library (NSSL) system file library called ULIB. It is published in three volumes. Each program write-up describes how to gain access to a particular routine and how to use it. Volume 1 Contents: 1. Solution of Non-Linear Systems. Determination of Roots of Polynomials. 2. Interpolation, Approximation and Smoothing. 3. Solution of Linear Systems and Eigenvalue/Eigenvector Analysis. 4. Numerical Integration (Quadrature). Volume 2 Contents: 5. Solution of Ordinary Differential Equations. 6. Solution of Partial Differential Equations. 7. Evaluation of Special Mathematical Functions. 8. Fast Fourier Analysis. 9. Statistical Analysis and Random Number Generation. Volume 3 Contents: 10. Special-Purpose Input/Output Routines. 11. Data Processing Utility Routines. 12. Computer Graphics. 13.File Manipulation, Text Editing, Program Preprocessing, and Debugging.