The objective of Chap. 1 is to introduce basic concepts that will be used for developing nonlinear finite element formulations in the following chapters. Depending on the level of the students or prerequisites for the course, this chapter or a part of it can be skipped. Basic concepts in this chapter include vector and tensor calculus in Sect. 1.2, definition of stress and strain in Sect. 1.3, mechanics of continuous bodies in Sect. 1.4 and linear finite element formulation in Sect 1.5. A MATLAB code for two- and three-dimensional finite element analysis with solid elements will reinforce mathematical understanding.