Short answers, pulled from the story.
The Second Boer War began on the 11th of October 1899, when Boer forces launched a preemptive offensive into British-held Natal and the Cape Colony. It ended with the Treaty of Vereeniging, signed on the 31st of May 1902.
The immediate causes were the dispute over voting rights for Uitlanders (foreign workers) in the Transvaal gold fields and British imperial ambitions in southern Africa. The discovery of gold at the Witwatersrand in 1884 drew tens of thousands of British migrants, but the Transvaal government required 14 years of residence before they could vote, fearing that concessions would cost the Boers control of their republic. Failed diplomatic talks at the Bloemfontein Conference in May 1899 and Kruger's ultimatum on the 9th of October 1899 triggered the outbreak of war.
26,000 Boer civilians died in British concentration camps from starvation and disease. A further 20,000 Indigenous Africans died in a separate system of 64 tented camps. Over 100,000 Boer civilians were forcibly relocated into these camps during the British scorched earth campaign.
Black Week refers to the period from the 10th to the 15th of December 1899, during which the British suffered three defeats in rapid succession. General Gatacre lost over 600 troops at Stormberg on the 10th; Methuen's force was repelled at Magersfontein on the 11th with 120 killed and 690 wounded; and on the 15th, Buller's 21,000 troops were turned back at the Second Battle of Colenso by 8,000 Boers under Louis Botha, losing 145 killed and 1,200 missing or wounded.
The Jameson Raid was a failed armed incursion in 1895, led by Leander Starr Jameson, in which a column of 600 men crossed from Bechuanaland toward Johannesburg intending to trigger an Uitlander uprising against the Transvaal government. The column was surrounded near Krugersdorp and surrendered after losing 65 killed and wounded. The raid united the Boers behind President Kruger, brought the Transvaal and Orange Free State into a military pact in 1897, and alienated Cape Afrikaners from Britain, making war much more likely.
The Treaty of Vereeniging was signed on the 31st of May 1902, after most Boer commanders accepted British terms to end the guerrilla war. The Transvaal and Orange Free State lost their independence and became British colonies. The Boers received reconstruction funds and a promise of limited self-government, which was granted in 1906 and 1907. In 1910, both territories were merged with Natal and the Cape Colony to form the Union of South Africa as a dominion of the British Empire.