If the universe is expanding and the distances of each galaxies get larger over time then why is our own galaxy (Milkyway) will collide with another galaxy (Andromeda) in the future?
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Because the rate of expansion depends on distance. Space expend like there is more space being added in between things. Thats what we call the stretching of space. So the things that are cloaser get carried away at a slower rate. The expansion becomes significant when you look at clusters of galaxies.
Galaxies also drift around and for those that are nearby their relative motion with respect to us massively outweighs the rate of expansion. Also as Andromeda gets closer gravity becomes more and more significant so whats going on is that we are falling towards each other. So gravity applies a force and so we have an acceleration. We can also treat the expansion as a kind of acceleration and so a force. The resulting motion is just the sum of the forces. And gravity over these distances wins. If you were to move Andromeda far away, the expansion of space would win.
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