Wikipedia
In J. R. R. Tolkien's fictional Middle-earth, the Dagor-nuin-Giliath (Battle under the Stars) is the second battle of the Wars of Beleriand, but the first involving the Noldor.
The Noldor following of Fëanor arrive in Middle-earth at the Firth of Drengist, and after burning their fleet, pass into Hithlum and encamp on the northern shore of Lake Mithrim. Their unforeseen arrival completely surprises Morgoth. This opportunity is somewhat compromised by Fëanor's ill-considered, wanton burning of the Telerin ships. The great fire alerts Morgoth and causes the Dark Lord to delay his plan to conquer Beleriand. He redeploys his forces to meet this new and unexpected threat.
Morgoth yet knows little of his foe's strengths and abilities. He hopes to destroy the Noldor under Fëanor before they can establish themselves. He attempts to concentrate several Orc forces to achieve this. An Orc-host is sent from Angband to attack over passes of the mountains of Ered Wethrin, and the Orc-host occupying East Beleriand and besieging the Havens of Círdan in the south is recalled to join in the attack. The Orcs of Morgoth far outnumber the Fëanorian Noldor, but the Orc-captains are unable to coordinate their attack and take advantage of their full, combined might. The Noldor are freshly empowered by the Light of Valinor, and using marvellous weapons and armour as well as the previously unseen cavalry they defeat the Orc forces in detail.
The first Orc-host of some 40,000 is quickly overwhelmed in Mithrim and retreats north through Ard-galen, with Fëanor in furious pursuit leading much of the cavalry. The Orc-captains of the south commanding an army reduced in strength from besieging the Havens of the Falas after the First Battle of Beleriand, move north to join the attack. Celegorm, leading the rest of the Fëanorian Noldor, waylays their line of march in the pass below Eithel Sirion, driving them into the Fens. Trapped between Celegorm's force and the Fens of Serech, the majority of the Orcs perish in a ten-day battle and the remnants try to flee back to Angband.
Fëanor, reckless in his wrath, pursues the Orcs across the plain of Ard-galen and became separated from his vanguard. At the north edge of the plain, on Dor Daedeloth, the Orcs make a stand and Gothmog leads his Balrogs forth from Thangorodrim to their aid. Fëanor stands his ground and long fights alone, until he is mortally wounded. Fëanor is rescued by his sons, but dies soon after.
The Dagor-nuin-Giliath is a bittersweet victory for the Fëanorian Noldor, as they destroy nearly all of Morgoth's forces in the several battles, but Fëanor is slain, and they had lost one of their princes.
In some tellings of the War of the Jewels, the Battle of Lammoth is counted as part of the Battle-under-Stars. In those tales, immediately following the rising of the Moon, Fingolfin and the second, greater Host of the Noldor arrive in Lammoth. There, they are attacked by Orcs which are sent by Morgoth to attack Fëanor in the rear, and they fight their first battle, the Battle of Lammoth. The Noldor are caught off-guard, and Fingolfin's son Argon is slain after a valiant fight that nevertheless dismays the enemy. Fingolfin and his host pursue the Orcs until they are completely destroyed, and then pass into Mithrim as the Sun first rises.