We begin our presentation of specific contact problems by dealing with the normal contact problem. In many tribological systems, the establishment of direct contact by a compressive force perpendicular to the contact plane is the basis of various tribological phenomena, such as friction or wear. This very comprehensive chapter is dedicated to plane, friction- and adhesion-free indentation of homogeneous, isotropic, elastic bodies. Starting from the general solution to the contact problem for single contacts of infinite length, we first consider specific contact problems with symmetrical or asymmetrical profiles. After that, periodic contacts and the influence of the actually finite extension of the contact bodies are discussed.