This chapter introduces some of the fundamental concepts of 3D geometry and 3D geometry processing. It focuses on the concepts that are relevant to the 3D shape analysis tasks. The first part of the chapter covers the elements of differential geometry that are used to describe the local properties of 3D shapes. The second part of the chapter defines the concept of shape, the transformations that preserve the shape of a 3D object, and the deformations that affect the shape of 3D objects. The chapter also describes some preprocessing algorithms, e.g. alignment, which are used to prepare 3D models for shape analysis tasks. In the field of shape analysis, the transformations associated with translation, rotation, and uniform scaling are termed shape-preserving. They are nuisance variables, which should be discarded. This process is called normalization. Normalization for translation and scale is probably the easiest one to deal with.