We do not know exactly. Within the part of the universe we can observe there seem to be at least 100 billion, but this could be an under estimate if you include dwarf galaxies that are too far away to be easily seen by even the Hubble Space Telescope.

Our universe seems to be infinite, or at the very least much larger than the current scale of the visible universe, so there are an unknown billions more galaxies beyond the limits to our visible universe.

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