The Third Voyage of James Cook, Vol 1, by James Cook. Part I.

Only months after his return from his mammoth Second Voyage, the Admiralty ordered Cook back to the Pacific, ostensibly to return Omai, a young man from Raiatea, to his homeland, but in fact to attempt the discovery of the Northwest Passage (a proposed route from the Pacific to the Atlantic north of Canada). 

Cook commanded HMS Resolution and was accompanied by Captain Clerke commanding HMS Discovery. After sailing to the Pacific via Tenerife, Cape Town and New Zealand, Omai was returned to his home, after which Cook became the first European to visit the Sandwich Islands (Hawaii) and then mapped the West Coast of North America. 

After many delays, he penetrated the Bering Strait, but was unable because of ice to proceed either East or West. He eventually returned to Hawaii, where Cook was killed by the natives. Following the death of Captain Clerke from tuberculosis, the ships eventually returned to Britain under the command of Captain Gore.

This first volume covers only the portion of the voyage up to the first visit to Hawaii.