The programming language Python

The Python home page is http://www.python.org">http://www.python.org
Python is an interpreted object oriented high level language. It is easy to learn and codes are easy to maintain. Python is growing fast and used in a variety of areas ranging from science to industry, business and finance (New York Stock exchange, Google, Yahoo, Disney Feature Length Animation, Industrial Light and Magic, Philips, IBM, Airbus, ... (read more
Python is free (and open) and platform independent.
Here is a (somewhat dated) 45-minute introduction (pdf) to Python aiming at people interested in text and data file processing and demonstrating the core of the Python language.
Alternatively, look at the official guide for python beginners

Usage

We use Python on a daily basis for

controlling applications and job execution on computational resources
analysing data
visualising data
performing numerical simulations (where we use established binary libraries and our own binary code for speed where necessary)
performing system administration tasks
building documentation and webpages
processing and analysing electronic submissions of student work
A (admittedly subjective) comment on use of Python for enterprise

IPython (Interactive Python): An advanced Python shell that provides command name and variable name completion (and many more useful features) (http://ipython.scipy.org/)
numpy (Numerical Python): Access to numerical libraries (provides matrix and array based computational features similar to MATLAB, IDL, ...) (http://www.scipy.org/numpy)
scipy (Scientific Python): Provides a variety of high level science and engineering modules together as a single package. SciPy includes modules for graphics and plotting, optimization, integration, special functions, signal and image processing, genetic algorithms, ODE solvers, and others. (http://www.scipy.org/)
matplotlib (Plotting Library, pylab): Emulates the Matlab plotting commands (only 2d at the moment). Very useful for people used to MATLAB. http://matplotlib.sourceforge.net/">matplotlib</a>:
vpython (Visual Python): Interactive 3d programming. Excellent for immediate visualisation of simple 3d scenes. (Based on OpenGL) (http://vpython.org/)

The "Numeric" package and the "Numarray" package will be replaced by the "NumPy" package in the long term future (we think). Numpy is a part of "SciPy", and used to be called scipy_core.
matplotlib requires either Numeric, Numarray or SciPy to be installed (and imports all commands from the MLab namespace from Numeric).
vpython requires Numeric or Numarray to be installed (and imports all commands of Numeric/Numarray).