What is the most distant known galaxy?
The farthest known galaxies are extremely bright galaxies, much brighter than our own Milky Way. They have to be, otherwise we could not see them at that distance. We think there are other galaxies near them that are dimmer, but we cannot see them.
The record right now is a galaxy at a redshift of about 7, which means that it is about 29 billion light years away. Redshifts are a way that Astronomers use to talk about the distance to far away galaxies - the bigger the redshift the further away the galaxy. We can't measure the distance directly, but the redshift can be measured from the light emitted by the galaxy, and redshifts can be converted into distances if you know how. Astronomers like to use redshifts in case we have to change the way we convert redshifts into distances, and also because there are lots of different ways to define the distance. How exactly this conversion is done depends on the history of the universe as a whole, and is something which has changed a lot in the last 10 years, so using redshifts seems safer to Astronomers. You can read about all the different types of distances in Astronomy here.
There was a team of Astronomers that reported seeing a galaxy at a redshift of about 10, but other Astronomers have looked into that claim and now most people think that that galaxy wasn't really that far away (some even think that it wasn't really a galaxy!). Looking out in distance is the same as looking back in time (because the light has taken a long time to get here), and Astronomers think that the galaxies we could see at redshifts of about 10 and bigger should be just forming. Before that (or further away) there probably weren't any galaxies yet.
The furthest galaxy you can see with your own eyes (without needing help from a telescope) is the Andromeda galaxy. It's so close that it really has the same redshift as us (0), but is actually about 2 million light years away!
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