Deep space research is an offshoot branch of astronomy, namely astronautics and space science which deals specifically with exploring the far distant areas of space. But, even in the context of this broad subject, there is very little agreement on the precise meaning of “deep space.” In some contexts, it’s used to describe both parallel bands of space which are beyond the Earth’s atmosphere, and which don’t show up on the geologists’ map of the Earth. But it can also be used in much more narrow contexts, such as in astronomy and astrobiology, to describe vast regions of emptiness beyond the Earth’s atmosphere which lie entirely beyond our understanding.
There is presently no known way to travel to these places, although theories abound, including travelling by vehicle from the moon to Mars (some scientists actually think this will someday be possible), visiting dark clouds of space, or even getting to the moon itself. One scientist recently proposed a mission to send unmanned explorers to explore the moon based upon an ancient Greek myth. The myth is that if a traveler visited the lost city of Atlantis, then that would mark the beginning of human civilization. Whether this story has any truth or not, there are many space agencies currently working on missions to explore the far reaches of the solar system and perhaps send people to explore the moon, and perhaps to try to get to Mars in the next 20 years or so.
For many years, NASA has been assisting European and American space agencies with plans for deep space exploration and several different types of manned deep space missions. Many believe that NASA is ideally suited to being one of the primary partners in exploring the unknown reaches of the solar system, and perhaps even to one day making a landing on the moon. Part of this can be done using robotic space probes or even human astronauts, depending on how successful the first deep space missions are.