Sage
is built out of nearly
100 open-source packages and features a unified
interface.
Sage can be used to study elementary and advanced, pure
and applied mathematics. This includes a huge range of mathematics,
including basic algebra, calculus, elementary to very advanced number
theory, cryptography, numerical computation, commutative algebra,
group theory, combinatorics, graph theory, exact linear algebra and
much more.
It combines
various software packages
and seamlessly
integrates their functionality into a common experience. It is
well-suited
for education and research.

The user interface is a
notebook in a web browser or the command line. Using the notebook,
Sage connects either locally to your own Sage installation or to a
Sage server on the network. Inside the Sage notebook you can create
embedded graphics, beautifully typeset mathematical expressions, add
and delete input, and share your work across the network.

The following showcase presents some of Sage's capabilities, screenshots and gives you an
overall impression of what Sage is. The examples show the lines of code in Sage on the left side,
accompanied by an explanation on the right. They only show the very basic concepts of how Sage
works. Please refer to the documentation material for more detailed
explanations or visit the library to see Sage in action.

**Video Introduction**to Sage by William Stein — first video of several explaining Sage, better than a bunch of screenshots...- Quickstart with Sage — explains basic concepts and gives you an impression of what Sage is.
- Sage Graphics — shows examples of useful plots and visualizations.
- Sage in Research — presents features useful for higher mathematics.
- Sage Benchmarks — compares speed or memory usage of Sage with other systems.

- Testimonials, Success Stories and News — read what others write about Sage.
- Screenshots — they give an impression how a Sage notebook looks like.
- Pictures — collection of images drawn by Sage.
- Interact — examples of Sage's interactive drawing capabilities.