In this seminar we begin with an overview of the numerical software packages developed in the past decades and the latest developments. We will take a look at the libraries and packages recently installed on SHARCNET systems. We will then focus on a number of selected libraries and packages and walk through them with examples. In particular, we would like to discuss the linear algebra packages in a collection of open source and proprietary libraries; the fastest FFT library FFTW; the peer reviewed C++ library Boost.Numeric.Odeint, intel ODE solvers and other packages for solving ordinary differential equations (ODEs); the packages for solving linear and nonlinear (partial differential) equations (PDEs); the packages for optimization problems; the GNU scientific library (GSL); the parallel random number generator SPRNG, and the arbitrary precision packages such as MPFUN. We will present simple examples in both C/C++ and Fortran for problems accessible to a general audience with a sound knowledge in numerical methods and working experience of C/C++ and/or Fortran.