LOTR full Balrog pursuit and conclusion (more in the description)

'Then tell us what you will, and time allows!' said Gimli.
'Come, Gandalf, tell us how you fared with the Balrog!'
'Name him not!' said Gandalf, and for a moment it seemed that a cloud of pain passed over his face, and he sat silent, looking old as death. 'Long I fell, he fell with me. His fire was about me. I was burned. Then we plunged into the deep water and all was dark. Cold it was as the tide of death: almost it froze my heart.'
'Deep is the abyss that is spanned by Durin's Bridge, and none has measured it,' said Gimli.
'Yet it has a bottom, beyond light and knowledge,' said Gandalf. 'Thither I came at last, to the uttermost foundations of stone. He was with me still. His fire was quenched, but now he was a thing of slime, stronger than a strangling snake.
'We fought far under the living earth, where time is not counted. Ever he clutched me, and ever I hewed him till at last he fled into dark tunnels. They were not made by Durin's folk, Gimli son of Glóin. Far, far below the deepest delvings of the Dwarves, the world is gnawed by nameless things. Even Sauron knows them not. They are older than he. Now I have walked there, but I will bring no report to darken the light of day. In that despair my enemy was my only hope, and I pursued him, clutching at his heels. Thus he brought me back at last to the secret of Khazad-dûm: too well he knew them all. Ever up now we went, until we came to the Endless Stairs.'
'Long has that been lost,' said Gimli. 'Many have said that it never made save in legend, but others say that it was destroyed.'
'It was made, and it had not been destroyed,' said Gandalf.
'From the lowest dungeon to the highest peak it climbed, ascending in unbroken spiral in many thousand steps, until it issued at last in Durin's Tower carved in the living rock of Zirakzigil, the pinnacle of the Silvertine.
'There upon Celebdil was a lonely window in the snow, and before it lay a narrow space, a dizzy eyrie above the mists of the world. The sun shone fiercely there, but all below was wrapped in cloud. Out he sprang, and even as I came behind, he burst into new flame, there was none to see, or perhaps in after ages songs would still be sung of the Battle of the Peak' Suddenly Gandalf laughed. 'But what would they say in song? Those that looked up from afar thought that the mountain was crowned with storm. Thunder they heard, and lightning, they said, smote upon Celebdil, and leaped back broken into tongues of fire. Is not that enough? A great smoke rose about us, vapour and steam. Ice fell like rain. I threw down my enemy, and he fell from the high place and broke the mountain-side where he smote it in his ruin. Then darkness took me, and I strayed out of thought and time, and I wandered far on roads that I will not tell.