Only thirty years have elapsed since E. Martensen published his well known paper proposing the surface vorticity boundary integral method for potential flow analysis. Generally regarded as the foundation stone, this paper has led to the establishment of a considerable volume of numerical methodology, applicable to a wide range of engineering problems, especially in the fields of aerodynamics and turbomachines. During this period we have also witnessed a technological transformation in the engineering world of immense proportions and of great historical significance. This has been based upon parallel advances in both theoretical and practical engineering skills which have been breath-taking at times. Theoretical methods, to which this book is dedicated, have undergone a renaissance spurred on by the rapid growth of computing power in response to the ever increasing demands of engineering hardware. The main characteristic of this new-birth has been a shift from the pyramid of classical methods to a whole host of numerical techniques more suited to direct modelling of real engineering problems. The explosion of this activity has been damped down only by the difficulties of transferring and absorbing into normal practice a technology which can, as in the case of many numerical methods, become highly personalised. After three decades there is a need for books which sift and catalogue and which attempt to lay out the new fundamental methodologies to suit the needs of engineers, teachers and research workers.