Most of the mathematical concepts we will be covering will lie in two areas: algebra and geometry. In a very coarse breakdown of the mathematics commonly used in physics, the remaining two broad areas would be foundations and analysis, the basic concepts of which will be presumed to be already familiar to the reader.

• Algebra is principally concerned with sets and arithmetic operations.
• Geometry is concerned with spaces and properties that are preserved under various transformations or equivalencies.

In our treatment, we will view algebra as a tool for revealing the structure of geometric objects, which are our primary focus.