With the growth of modern computing power it has become possible to apply far more mathematics to real problems. This has led to the difficulty that many people who have been working in various jobs suddenly find themselves not understanding the modern processing which is being applied to their own professional field. It also means that the people presently being trained in these subjects need to understand a much wider range of mathe­ matics than in the past. It is to both of these groups that this book is addressed. The major objective is to present the reader with the basic mathematical understanding to follow the new developments in their own field. The mathematics in this book is based on the need to understand signal process­ ing. The modern work in this area is mathematically very sophisticated and our purpose is not to train professional mathematicians but to make far more of the literature accessible. Since this book is based on courses devised for Racal Geophysics there is clearly going to be a bias towards the applications in that area, as the title implies. It is also true that the bibliogra­ phy has been chosen in order to aid the reader in that field by pointing them in the direction of recent applications in geophysics.