The first five chapters of this book form an introductory course in piece- wise-linear topology in which no assumptions are made other than basic topological notions. This course would be suitable as a second course in topology with a geometric flavour, to follow a first course in point-set topology, andi)erhaps to be given as a final year undergraduate course. The whole book gives an account of handle theory in a piecewise- linear setting and could be the basis of a first year postgraduate lecture or reading course. Some results from algebraic topology are needed for handle theory and these are collected in an appendix. In a second appen- dix are listed the properties of Whitehead torsion which are used in the s-cobordism theorem. These appendices should enable a reader with only basic knowledge to complete the book. The book is also intended to form an introduction to modern geo- metric topology as a research subject, a bibliography of research papers being included. We have omitted acknowledgements and references from the main text and have collected these in a set of "historical notes" to be found after the appendices.