It is a mystery why anyone would write a textbook on algebra and routinely fail to define the subject. So what is algebra? Algebra is the language of higher mathematics, but it is not just another language. Algebra is an abstract symbolic language plus reasoning; it is a language with the rules of logic built-in. The structure of algebra: assumption-deduction-conclusion, transforms the language into not only a tool for reasoning in that it enables the connection of one statement to another, but also an elegant tool for conveying information that is more precise and concise than any written description of phenomena can possibly be; one important example is the algebraic formulation of the laws of nature.