Intergalactic travel is space travel between galaxies. Due to the enormous distances between the Milky Way and even its closest neighbors, any such venture would be far more technologically demanding than interstellar travel. Intergalactic distances are roughly one-million fold (six orders of magnitude) greater than their interstellar counterparts. The technology required to travel between galaxies in a feasible way and within a human lifetime is far beyond humankind's present capabilities, and is currently only the subject of speculation, hypothesis, and science fiction.
The difficulties of intergalactic travel and a possible solution 
Intergalactic travel, as it pertains to humans, is entirely beyond the capabilities of current engineering and discussion of the subject is speculative to the point of becoming science fiction. Due to the enormity 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 condemns any attempt to travel to other galaxies to a journey of millions of years. However, while it takes light approximately 2.54 million years to traverse the gulf of space between Earth and, say, the Andromeda Galaxy, it would take a much shorter amount of time from the point of view of a traveler at close to the speed of light due to the effects of time dilation; the time experienced by the traveler depending both on velocity (anything less than the speed of light) and distance traveled (length contraction). Intergalactic travel is therefore possible, in theory, but only at extreme relativistic speeds and only from the point of view of the traveller.
Another difficulty would be to navigate the spacecraft to the target galaxy and succeed in reaching a chosen star, planet or other body, as this would require a full understanding of the movement of galaxies which has not yet been attained. There is also the considerable problem, even for unmanned probes, that any communication between the craft and its home planet can still only travel at the speed of light, which may require millions of years to traverse the colossal distances involved. Even if another galaxy could be reached there seems be no way for the information to be transmitted home in any meaningful way.
The Alcubierre drive is the only feasible, albeit highly hypothetical, concept, that is able to impulse a spacecraft to speeds faster than light. The spaceship itself wouldn't move faster than light, but the space around it would, in theory allowing practical intergalactic travel. There is no known way to create the space-distorting wave this concept needs to work, but the metrics of the equations comply with relativity and the limit of light speed.
Natural intergalactic travel 
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. One theory for their existence is 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 is the gravitationally driven merging of the milky way with nearby galaxies or star clusters. For instance it is known that The Andromeda galaxy (larger than our Milky Way) and the Milky Way are going to "collide" approximately four billion years from now. Computer simulations show many stars being ejected from the resulting larger galaxy. It is theorized that the Milky Way has been growing in this manner for billions of years through the capture of smaller stellar groups. By 2010, sixteen hypervelocity stars had been observed. Intergalactic dust is also thought to be ejected from galaxies, and has been observed in intergalactic space.
Nearest galaxies 
See also 
- Intergalactic space, Intergalactic stars, Intergalactic dust
- Galaxies in fiction
- Satellite galaxy
- Dwarf galaxy
- Science fiction
- Star Trek's Warp Drive: Not Impossible from space.com
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- Ray Villard - The great escape intergalactic travel is possible, 24 May 2010, DiscoveryNews