The first two tutorials are excellent for new users, and can be assigned to students as homework to learn Mathematica outside of class time.
Hands-on Start to Mathematica
Follow along in Mathematica as you watch this multi-part screencast that teaches you the basics—how to create your first notebook, calculations, visualizations, interactive examples, and more.
What's New in Mathematica 10
Provides examples to help you get started with new functionality in Mathematica 10, including the predictive interface.
How To Topics
Access step-by-step instructions ranging from how to create animations to basic syntax information.
Search Wolfram's large collection of materials for example calculations or tutorials in your field of interest.
Teaching with Mathematica
Mathematica offers an interactive classroom experience that helps students explore and grasp concepts, plus gives faculty the tools they need to easily create supporting course materials, assignments, and presentations.
Resources for educators
Mathematica for Teaching and Education—Free video course
Learn how to make your classroom dynamic with interactive models, explore computation and visualization capabilities in Mathematica that make it useful for teaching practically any subject at any level, and get best-practice suggestions for course integration.
How To Create a Lecture Slideshow—Video tutorial
Learn how to create a slideshow for class that shows a mixture of graphics, calculations, and nicely formatted text, with live calculations or animations.
Wolfram Demonstrations Project
Download pre-built, open-code examples from a daily-growing collection of interactive visualizations, spanning a remarkable range of topics.
Rather than requiring different toolkits for different jobs, Mathematica integrates the world's largest collection of algorithms, high-performance computing capabilities, and a powerful visualization engine in one coherent system, making it ideal for academic research in just about any discipline.
Resources for researchers
Mathematica for University Research—Free video course
Explore Mathematica's high-level and multi-paradigm programming language, support for parallel computing and GPU architectures, built-in functionality for specialized application areas, and multiple publishing and deployment options for sharing your work.