This book is part of a series designed to provide engineering students in colleges and universities with a mathematical toolkit, each book including the mathematics in an engineering context. Worked examples and problems with answers are included. It is aimed primarily at HNC/HND students and first-year undergraduates. Thus the mathematics assumed is that in BTEC National Certificates and Diplomas or in A level. The pace of development has been aimed at the notional reader for whom mathematics is not their prime interest or "best subject" but who need the mathematics in their other studies. This book is concerned with the Fourier series and an introduction to the Fourier transform and their application in engineering. It does need some mathematics which might not have been covered in the BTEC National or A level courses. A familiarity with basic algebra, complex numbers and calculus is assumed. An appendix giving supportive mathematics is included. The aim of the book has been to include sufficient worked examples and problems to enable the reader to acquire some understanding and proficiency in the use of Fourier series and transforms in dealing with periodic waveforms which are non-sinusoidal or distored sinsusoidal, and signals which are non-repetitive.