* LAPACK (BLAS is there too) http://www.netlib.org/lapack/explore-html/
* QUADPACK (quadrature integration) http://www.netlib.org/quadpack/
* MINPACK (nonlinear solvers) http://netlib.org/minpack/index.html
* ODEPACK (ordinary differential equations) http://netlib.org/odepack/index.html
Most of the textbooks on numerical methods are not very approachable, but Carl Meyer's Matrix Analysis and Applied Linear Algebra text is a good start, as are Gilbert Strang's books.