Due to the lack of space propulsion technology and space navigation technology that can accelerate at high speeds in a short time, it is well-known that mankind does not currently have technology to realize a journey to other star systems. This book explains galaxy exploration by combining field propulsion based on the physical structure of space-time and a new navigation theory. A field propulsion system is propelled without mass expulsion. The propulsive force as a pressure thrust arises from the interaction of space-time around the spaceship itself; this causes the spaceship to propel against the space-time structure. Firstly, from the physical and engineering point of view, the propulsion principle and propulsion theory of field propulsion are explained. As a typical example of field propulsion, the space drive propulsion system includes its theory, the registered patent, and the latest development from the viewpoint of cosmology and astrophysics. Secondly, for galaxy exploration, navigation technology such as a wormhole that bypasses the wall of light speed, not propulsion technology, is indispensable. A method for overcoming the light barrier (the seeming wall-of-light in 4-D space-time), or a hyperspace navigation theory to jump the light-barrier, is explained. Combining the space propulsion system and the navigation system makes it possible to perform a realistic galaxy exploration.The reader will not only get a good introduction to the science and technology of field power and propulsion physics, but also to the possibility of interstellar navigation.