The nearest star to the Earth is the Sun, the great ball of fire in the sky. Some people forget the Sun is actually a star. It is referred to as a dwarf star compared so absolute giants out there such as UY Scuti, the current record holder at 1708 times the size of our sun.
Proxima Centauri is one three stars that make up the Alpha Centauri / Rigil Kentaurus multiple star system. Alpha Centauri A and B are positions three and four in the list. They are located in the southern constellation of Centaurus. Proxima is a red dwarf star which in addition to being the nearest star to us, its also the nearest star that has an orbiting extra solar planet. The other two are yellow stars similar to our own star. Alpha Centauri A is slightly larger than our Sun but not by much.
Barnards Star is the closest star in the Northern Hemisphere and situated in the constellation of Ophiuchus, the thirteenth sign of the Zodiac. It is named after E.E. Barnard who although he didn't discover it, he was known for the discovery of the high proper motion of the star. It is situated about 5.9 light years away from Earth.
Luhman 16 is a small brown dwarf star in Vela, the closest of its type if you exclude nemesis. Nemesis is a theorectial star that is believed to affect the an area of space 1 light year away known as the Oort cloud and cause the comets in the belt to head towards us. It is a binary star system but I have only detailed one of the stars on this site. Therefore you could say they are the 6th and 7th closest stars to us. The name for the star comes from its discoverer, Kevin Luhman from the Pennsylvania University in the United States.
Wise 0855-0714 is located in Hydra and is a small and not very luminous star that was discovered recently. It is not a star to be seen in the night sky. It was discovered by Kevin Luhman who also discovered the sixth most closest star to us.
Anyone who knows a lot about Star Trek will know of the famous fictional battle, Battle of Wolf 359 which resulted in destruction of the Federation fleet at the hands of a Borg Cube. The fact that the star is close to Earth was the reason for its being chosen. At that time of the series, Luhman and Wise stars had not yet been discovered. The star is located in the constellation of Leo.
Lalande 21185 is the brightest red dwarf in the northern hemisphere and only third brightest in the night sky. It is too dim to be seen in the night sky with the naked eye but probably be seen with a good telescope or binoculars. It can be located in the Ursa Major northern constellation.
The tenth closest is Sirius, the Dog star in the constellation of Canis Major and it is also the brightest star in the night sky. Sirius is a double star and the companion star would amount to being the 11th brightest.
The universe is so vast that we can't see the edge of the galaxy. The most distant star covered on this site is R136a, in the constellation of Dorado. The star is not in our galaxy but is in the Tarantula nebula in the satellite galaxy of the Large Magellanic Cloud. The imaginatively name HE 0437-5439 is moving out of the milky way Galaxy at a speed of three times the orbital speed of the Sun. Some stars will appear that they are further out on this website but the data should be assumed to be incorrect.