This book presents the theoretical and practical development of a new algorithm for generating full 3D surface maps of prior unknown and unstructured environments. It introduces methods for extraction of surfaces from 3D range images, homogenization of representations of irregularly sampled surfaces, alignment of set of surfaces relative to the map and consistent unification of the same object's overlapping surfaces. The presented surface-based map of the environment is built incrementally. The resulting map represents the environment via set of individual surfaces. Objects in the map are represented via their exact shapes. The presented mapping technique is illustrated in the context of mobile robotics application. The book also includes the flow charts of the introduced algorithms for online implementation. Therefore, the book will serve as a useful reference for online mapping applications. The resulting full 3D map can be used in a wide variety of navigation applications, including path planning and collision avoidance.