Many years ago it was suggested by Professor Robert E. Gibson to a group of colleagues to write a book on the theory of consolidation, as the theory of poroelasticity was then called, on the lines of the classical treatise by Carslaw and Jaeger on the Conduction of Heat in Solids. Some of us have written parts of suchbook, notably Professors Gerard De Josselin de Jong and Robert L. Schiffman, but it appeared that the task was too large, perhaps also because some of us got other interests, and the difficulties in completing solutions required so much mathematical effort that many papers had to finish by announcing that more results would be published in later papers, which never actually occurred. In the meantime solutions of many problems were published, and now that I have retired from university duties there is some time to complete and update existing solutions, and publish the material in the form of this book. It also helped that my Australian colleagues Professors Booker, Carter and Small drew my attention to numerical techniques for inverse Laplace transforms, especially Talbot’s method, which is a simple and effective method for the solution of many problems, so that the promises made earlier for detailed solutions can now be fulfilled. On the other hand, so many solutions of problems have now been published by authors from many places in the world that this book is far from being complete, and merely gives a personal view of the main aspects of the theory, some powerful solution methods, and examples of solutions.