The aim of this book is to enable talented students to tackle the sort of problems on algebra which are set in mathematics competitions. Topics include surds, digits, base arithmetic, polynomials, simultaneous equations, sequences, sums, functional equations and algebraic methods in geometry. Books in the Handbooks series are aimed particularly at students in secondary school who are interested in acquiring knowledge and skills which are useful for tackling problems, such as those posed in the competitions administered by the UKMT and similar organisations.  Like the previous volumes in the Handbooks series, this book provides ready access to directly relevant material. All these books are characterised by the large number of carefully constructed exercises for the reader to attempt, together with full solutions.