Over the past decades, the boundary element method has emerged as a versatile and powerful tool for the solution of engineering problems, presenting in many cases an alternative to the more widely used finite element method. As with any numerical method, the engineer or scientist who applies it to a practical problem needs to be acquainted with and understand its basic principles to be able to apply it correctly and be aware of its limitations. It is with this intention that we have endeavored to write this book: to give the student or practitioner an easy-to-understand introductory course to the method so as to enable him or her to apply it judiciously. As the title suggests, this book not only serves as an introductory course but also covers some advanced topics that we consider important for the researcher who needs to be up-to-date with new developments. This book is the result.