This is an official center for all documentation to NumPy and SciPy. Those are two independent packages, but from historical reasons, the documentation for both of them is on this page. Unfortunately, there is still a lot of outdated documentation to predecessors (or older versions of NumPy) floating on the internet, however this site is the only official documentation. If you are confused about the predecessors of NumPy, read a History of SciPy -- a summary of the events that led to SciPy and NumPy.
The NumPy/SciPy Summer Documentation Marathon 2008 is in progress! See (and help write) the improved docstrings.
NumPy
NumPy is a standalone package that provides array manipulation tools for python. In the future, the NumPy is going to have a homepage at numpy.org. In the meantime, you can find all the documentation here.
Tutorial: if you are new to NumPy, start reading this tutorial.
Guide to NumPy (fee-based until SciPy 2008), by Travis Oliphant the lead developer of NumPy. This e-book is a complete reference to NumPy, this is a nice documentation to all features of NumPy, however, you can only read first 2 chapters for free, you need to buy it in order to read the rest.
Numpy Functions by Category: A list of the functions in NumPy organized by task, with links to the Example List with documentation.
Numpy Example List: large database demonstrating most of the NumPy functionality, read this if you prefer to learn by examples. A version without doc strings is also available.
NumPy for MATLAB® Users: An overview of the basics of NumPy for those familiar with MATLAB® (you can read this even if you never used matlab before, this document contains a review of NumPy)
Porting to NumPy: Provides stories and examples of porting applications to use NumPy.
NumPy API documentation: Autogenerated using endo
NumPy C Application Programmer's Interface: if you want to interface your code to Python and NumPy.
NumPy Distutils User's Guide: shows how to write a setup.py for your own project
Documentation from NumPy's predecessor, Numeric. Much of it still applies, but replace Numeric with numpy in all import statements.
Scipy
The SciPy library is built to work with NumPy arrays, and provides many user-friendly and efficient numerical routines such as routines for numerical integration or optimization.
Tutorial: If you are new to SciPy, start with this tutorial.
Tutorial II (pdf): This is a very nice tutorial, but it was written in 2004, so it doesn't cover new features.
Examples: Very few (at the moment) examples of SciPy usage
SciPy packages: An overview of the packages available in SciPy, unfortunately very few are currently documented
SciPy API documentation: Autogenerated using endo
Citing SciPy: How to properly cite the SciPy tools in a paper or presentation
Trinity: An example calculation (computing the energy released by the Trinity atomic bomb test).
Other
Other (mostly unofficial) documentation to NumPy and SciPy.
FAQ. Answers to the most frequently-asked questions.
A course on NumPy/SciPy by Dave Kuhlman
A tutorial focused on interactive data analysis for astronomy, but of generic utility to most scientific users.
Scientific Computing with Python (registration required) A one day tutorial presented by Eric Jones and Travis Oliphant in October 2005
Weave: inclusion of C/C++ code in Python
Porting to NumPy: Provides stories and examples of porting applications from Numeric/Numarray to NumPy.
PerformanceTips. How to maximize the speed of your code using numpy/scipy.
Proposed improvements to NumPy/SciPy that need discussion.