Superquadrics are a family of parametric shapes that have been used as primitives for shape representation in computer vision and computer graphics. They can be used for modeling tapering and bending deformations and are recovered efficiently by a stable numerical procedure. This document introduces the superquadric library, SQ_lib, developed at the GRASP Lab at the University of Pennsylvania. The manual is organized into three parts. The first part provides the reader with a description of superquadrics models and deformations that can be performed. Furthermore, it introduces the coordinate systems conventions which are used in the library. The second part presents some examples of applications on how one can use the functions defined in the library. It also lists utility programs which have been developed while conducting research. They provide a good source of examples for the application of the library. Finally, the last part describes the datatypes and each of the functions which are supported in the library. The library itself is organized in two sets Fundamental and Auxiliary functions. A quick reference to all the functions and an index is provided. Some of the functions and examples supplied perform data preprocessing and are connected to the PM image description also available from the GRASP Lab. These functions are provided in isolation from the remaining body of the library and can easily be excluded in the actual compilation of the library. Furthermore, routines for the visualization of the data, using X11, are also provided.