In this book the application of the boundary element method to the solution of the Laplace equation is examined. This equation is of fundamental importance in engineering and science as it describes different types of phenomena, inclu- ding the groundwater flow applications highlighted in this book. Special subjects such as numerical integration, subdi- visionof the domain into regions and other computational aspects are discussed in detail in the first chapters. To demonstrate the accuracy and efficiency of the boundary ele- ment method, results obtained when solving the Laplace equa- tion have been compared against known analytical solutions. Other chapters deal with problems such as steady and unstea- dy flow in addition to infiltration problems. The applica- tions demonstrate that the boundary element method provides a powerful solution technique which can be effectively ap- plied to solve this type of problem.