Structures and engineering works are normally established on the physical earth (known as the plane system) whereas other surveying/geodesist structures such as the global navigation satellite system (GNSS) to which global positioning system (GPS) belong orbit some 20,000 km above the surface of the Earth. In both cases, engineering and surveying/geodesy, it is essential that the computations be done in the proper system. For example, the engineers will undertake their computations on a plane defined by two perpendicular axes (x and y) whereas the geodesist or surveyor will use an ellipsoid of revolution (imagine an egg rotated) to get the positions from the satellites. This Chapter starts by introducing general formulae before presenting these two coordinate systems and presents the methods of converting from one system to another. Knowledge and skills from this fundamental chapter is a necessity for the subsequent chapters as most if not all computational surveys for engineering and surveying work will be undertaken in either of these two systems. The aim of the first half of this book is to introduce the student to the fundamentals of survey computations and, in particular, the accuracies involved in arithmetic computations and the proper use of mathematical results. The person performing the calculations is called the computer. A basic electronic calculator with hardwired trigonometric functions is required for this part of the course. The second part of the course, using these fundamental methods, introduces the student to the solution of some basic survey calculations, and to solve particular survey problems.