Fortran Libraries

All of the following are free:

• Big Integers Module
• BLAS
• EISPACK
• GAMS--NIST Guide to Available Math Software
• Harwell-Boeing collection (sparse matrices)
• Interval Arithmetic Package
• LAPACK
• LINPACK
• MINPACK
• MUDPACK
• Multiple Precision Arithmetic Package
• NCAR Mathematical Library
• The Netlib collection of mathematical software, papers, and databases.
• ODEPACK
• SLATEC
• SPECFUN
• STARPAC
• StatLib statistical library
• TOMS

Here is a whole bunch of links to software repositories in North America.

The NCAR math library contains some of the routines listed above and many more.

The following are not free:

• Fluid Dynamics library: FDLIB

  
  FDLIB is a comprehensive Fortran 77 software library covering a wide spectrum of fundamental and applied topics in fluid dynamics ranging from potential flows, to viscous flows, to vortex flows, to hydrodynamic stability, to multi-phase flows, to aerodynamics, to many other disciplines.

  The codes are suitable for self-study, classroom instruction, as well as academic and industrial research. FDLIB 1.0 consists of 233 utility subroutines and simulation programs. A comprehensive User's Guide accompanies the source codes.

  The library is produced and distributed by the Phaedrus Group. For further information, please click on FDLIB.

• MatheMatrix, Out-Of-Core, Dense, Direct Solver matrix algebra libraries
• Numerical Recipes