Short answers, pulled from the story.
The Anglo-Persian Oil Company was founded on the 14th of April 1909 by the Burmah Oil Company as a subsidiary, following the discovery of oil at Masjed Soleiman in Persia on the 26th of May 1908. William Knox D'Arcy had originally obtained the oil concession from Mozaffar al-Din Shah Qajar in 1901, and Burmah Oil had acquired most of D'Arcy's rights before the discovery.
The British government purchased 51 percent of the company in 1914 to secure a guaranteed oil supply for the Royal Navy, which Winston Churchill was modernizing by replacing coal-fired ships with oil-fueled vessels. Churchill also sought to reduce British dependence on Standard Oil and Royal Dutch Shell. The government paid for its stake by injecting new capital into APOC.
Iranian workers in the AIOC oil fields earned 50 cents a day with no vacation pay, no sick leave, and no disability compensation. They lived in a settlement called Kaghazabad, or Paper City, which lacked running water, electricity, and basic amenities. The AIOC had promised under the 1933 agreement to improve pay and build schools, hospitals, and roads, but did not fulfill those promises.
The Iranian parliament voted to nationalize the AIOC and its holdings in March 1951, and Mossadegh was elected prime minister in April 1951, becoming the champion of nationalization. He broke off negotiations with the AIOC in July 1951 and oversaw the creation of the National Iranian Oil Company to take control of Iran's oil resources and infrastructure.
Operation Ajax was the CIA's plan to remove Mohammad Mossadegh from power; Britain's parallel operation was called Operation Boot. The CIA used intelligence from British sources and paid politicians, soldiers, mobsters, and journalists to destabilize Iran. General Fazlollah Zahedi led tanks to Mossadegh's residence and arrested him for treason. On the 21st of December 1953, Mossadegh was sentenced to three years of solitary confinement in a military prison.
The company renamed itself the Anglo-Iranian Oil Company in 1935 and then British Petroleum in 1954. After nationalization and the coup, BP was required to join a consortium called Iranian Oil Participants Ltd, in which it held a 40 percent share alongside Royal Dutch Shell, Gulf Oil, Compagnie Française des Pétroles, and the four Aramco partners. The Shah signed the consortium agreement on the 29th of October 1954.