Intergalactic travel is the term used for hypothetical manned or unmanned travel between galaxies. Due to the enormous distances between our own galaxy the Milky Way and even its closest neighbors
The technology required to travel between galaxies is far beyond humanity's present capabilities, and currently only the subject of speculation, hypothesis, and science fiction.
However, scientifically speaking, there is nothing to indicate that intergalactic travel is impossible. There are in fact several conceivable methods of doing it; to date there have been a few people who have studied intergalactic travel in a serious manner.
Due to the size of the distances involved any serious attempt to travel between galaxies would require methods of propulsion far beyond what is currently thought possible in order to bring a large craft close to the speed of light.
According to the current understanding of physics, an object within space-time cannot exceed the speed of light, which means an attempt to travel to any other galaxy would be a journey of millions of earth years via conventional flight.
Manned travel at a speed not close to the speed of light, would require either that we overcome our own mortality with technologies like radical life extension or traveling with a generation ship. If traveling at a speed closer to the speed of light, time dilation would allow intergalactic travel in a timespan of decades of on-ship time.
These challenges also mean a return trip would be very difficult.
Voyages to other galaxies at sub-light speeds would require voyage times anywhere from hundreds of thousands to many millions of years. To date only one design such as this has ever been made.
Theorized in 1988, and observed in 2005, there are stars moving faster than the escape velocity of the Milky Way, and are traveling out into intergalactic space. There are several theories for their existence. One of the mechanisms would be that the supermassive black hole at the center of the Milky Way ejects stars from the galaxy at a rate of about one every hundred thousand years. Another theorized mechanism might be a supernova explosion in a binary system.