This thesis explores the possibilities of doing mathematical problems involving algebra on a computer. A language is designed which allows names to occur as unknown quantities. This language has all the facilities of a general purpose language such as IMP, but is designed to be used inter-actively by a user at a console. The language also includes instructions which cause the usual algebraic operations to be applied to expressions. These operators include simplification, differentiation, but not integration. A brief survey is given of other languages in the field, with comments on their capabilities and restrictions. The second part of the thesis describes how the language is implemented. An interpreter is used. Statements of the language are analysed syntactically and then obeyed. Algebraic expressions are stored in byte arrays, using a type of prefix Polish notation. Finally the language is reviewed in the light of recent work done in the field, and suggestions are made for a further version.