The first complete ascent of Mt Cook was made by New Zealanders Tom Fyfe, George Graham (NZAC) and Jack Clark(e) on Christmas Day 1894.
The NZAC Alpine Journal of May 1895 Vol II, No 7 provides an “Extract from Mr T C Fyfe’s Account in the Otago Daily Times of February 21st, 1895“ as uploaded here in PDF format (16mb) (also included is an account of Zurbriggen’s 2nd ascent)
“I am afraid that the reckless way in which we romped over those last rocks was very fool-hardy, but one would indeed need to be phlegmatic not to get a little excited on such an occasion. The slope of the initial ice-cap was easy and only required about 100 steps, which were quickly cut, and at 1:30 on Christmas Day we exultantly stepped on to the highest pinnacle of the monarch of the Southern Alps.”
The first ascent of Mt Cook by a woman was completed by Australian Freda du Faur 3 December 1910. An anniversary celebration was held in 2010. Biography and climbing history provided for this can be viewed here: Freda du Faur Centenary
An account of the first ascent of the South Ridge of Mt Cook 1948, by Harry Ayres, Edmund Hillary, Mick Sullivan and Ruth Adams. Also information on the Ruth Adams rescue that followed the completion of this climb.