The book is a self-contained introduction to the results and methods in classical invariant theory.

Introduction; Notes to the reader; A brief history; Acknowledgements; 1. Prelude - quadratic polynomials and quadratic forms; 2. Basic invariant theory for binary forms; 3. Groups and transformations; 4. Representations and invariants; 5. Transvectants; 6. Symbolic methods; 7. Graphical methods; 8. Lie groups and moving frames; 9. Infinitesimal methods; 10. Multi-variate polynomials; References; Author index; Subject index.