Why doesn't the galaxies collide due to gravitational attraction and why doesn't all the matter in the universe stick together due to gravitational attraction?
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Galaxies do collide due to gravity. They don't stick together exactly, because they're not solid bodies; but they do often merge. See this article on the NASA website, for example.
Glorfindel
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S. McGrew
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Galaxies do merge, not collide exactly. They aren't physical bodies like planets and stuff. They are a collection of a vast number of stars orbiting around a common centre. For example, the milky way and the andromeda will merge into one galaxy in the future
However another thing to consider is the expansion of the universe... this causes most of the galaxies to move further away from each other but there maybe mergers like the one given above. Overall, this accelerating expansion of the universe due to dark energy is enough to overcome the gravity between the galaxies though on small scales, there can be cases where they merge
Michael Seifert
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