AFEPack is a general-purpose C++ library for numerical solutions of partial differential equations. With over two decades development, AFEPack has been successfully applied for scientific and engineering computational problems in a variety of areas such as computational fluid dynamics, electronic structure calculations, computational micromagnetics. In this paper, design philosophy of the library, algorithms and data structures used in the discretization of governing equations, numerical linear algebra for the discretized system, as well as the pre-processing and post-processing of the simulations, will be described systematically for the AFEPack. The realization of two main features of the library, i.e., adaptive mesh methods and parallel computing, will be introduced in detail. The potential of the library for large scale scientific/engineering problems would be demonstrated by several examples. The future works on developing the library will also be discussed.