NumPy (source code) is a Python code library that adds scientific computing capabilities such as N-dimensional array objects, FORTRAN and C++ code integration, linear algebra and Fourier transformations. NumPy serves as a required dependency for many other scientific computing packages such as pandas.
Blaze is a similar, but separate, ecosystem with additional tools for wrangling, cleaning, processing and analyzing data.
SciPy Lecture notes goes into the overall Python scientific computing ecosystem and how to use it.
The SciPy Cookbook contains instructions for various SciPy packages that were previously hosted on the SciPy wiki.
Lectures in Quantitative Economics: SciPy provides a good overview of SciPy compared to the specific NumPy project, as well as explanations for the wrappers SciPy provides over lower-level FORTRAN libraries.
A plea for stability in the SciPy ecosystem presents concerns from one scientist's perspective about how fast the Python programming ecosystem changes and that code can become backwards incompatible in only a few years. The issue is that many science projects last decades and therefore cannot follow the rate of change as easily as typical software development projects.
From Python to NumPy is an awesome resource that shows how to use your basic Python knowledge to learn how to do vectorization with NumPy.
The ultimate beginner's guide to NumPy explains how to install and import NumPy, then digs into using arrays for computation and how to perform operations that get the results you need for your data analysis.
Python NumPy Array Tutorial is a starter tutorial specifically focused on using and working with NumPy's powerful arrays.