This is the first in a series of modular mathematics books for use by students wishing to gain academic qualifications beyond GCSE. An AS subject in mathematics requires two modules and an A-level needs four modules. This book can be used for the pure mathematics content of AS subjects combining pure mathematics with mechanics or with statistics. Now that GCSE courses have been introduced it can no longer be assumed that all students start with the algebraic skills and geometric knowledge that used to be expected. Many students now moving on to sixth-form colleges come from a variety of backgrounds, including those who wish to embark on an AS or A-level course from intermediate-level GCSE. In much the same way that multiplication tables are the tools needed to build a mathematics course from 11 to 16, skills in algebraic techniques are the tools necessary for building a body of further mathematical knowledge. This book starts with work designed to help those students acquire a facility in using algebra. The exercises start with straightforward questions. The more sophisticated exam-type questions are given in consolidation sections which appear at regular intervals throughout the book, and are intended for use later, to give practice when confidence and sophistication have been developed. The consolidation sections also include a summary of the work in preceding chapters and a set of multiple choice questions which are useful for self-testing, even if they do not form part of the examination to be taken.