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We know that the Andromeda Galaxy is moving towards the Milky Way and vice versa, so there will be a collision. Because of the vast space between them, the stars as they are defined will not themselves come into contact until much later if at any time at all.
My question is whether Andromeda has had a collision prior to this 4 billion year inevitability.
Galaxies grow through cosmic time by accretion of the surrounding matter. Some of its mass increase happens through smooth accretion of gas, but much also happens through merging with small clumps of dark matter, gas, and stars, called satellite galaxies. This is called "minor merging".
If merging galaxies are similar in size, it's called major merging. Most large galaxies have gone through of the order of one major merger through its life (Man et la. 2014), but whether or not it happened for Andromeda, we cannot know for certain.
However, if you take a look at Andromeda, you'll see that it has quite a large bulge, i.e. the central, reddish part of the galaxy. This region is dominated by stars with a more "chaotic" velocity patterns. That is, their paths aren't "rotation-dominated" (lie in the disk), but more "dispersion-dominated" (leave the disk). To achieve such velocities, the system has to be disturbed by infalling matter, so a large bulge is probably a signature of a major merger. Investigating the velocity patterns of Andromeda, Dorman et al. (2015) find that it has had a much more violent history than the Milky Way, and in fact models by Davidge et al. (2012) and simulations by Hammer et al. (2010) of the history of Andromeda suggest that 8-9 billion years ago, Andromeda went through a major merger.
Note however that a large bulge can also be explained, at least in cosmological simulations, by a more smooth and "cold" accretion, i.e. gas that doesn't get shock-heated (Dekel et al.)
