Short answers, pulled from the story.
The Battle of the Atlantic ran for more than five years, from the outbreak of war in September 1939 until the German surrender in May 1945. It has been described as the longest continuous military campaign of the Second World War.
Churchill wrote that the U-boat peril was "the only thing that really frightened me during the war," adding that he was even more anxious about the Battle of the Atlantic than he had been about the Battle of Britain.
3,500 Allied merchant ships and 175 Allied warships were sunk in the Atlantic. In return, 783 German U-boats and 47 German surface warships were lost, including 4 battleships, 9 cruisers, 7 raiders, and 27 destroyers.
The Happy Time, or Die Glückliche Zeit, was the period from June to October 1940 when U-boats operating from newly captured French bases sank over 270 Allied ships. U-boat aces such as Günther Prien, Otto Kretschmer, and Joachim Schepke became national heroes in Germany during this period.
Black May refers to May 1943, when 43 U-boats were destroyed in a single month, 34 of them in the Atlantic. This represented 25% of the U-boat Arm's total operational strength. Dönitz called off operations in the North Atlantic that month, admitting "We had lost the Battle of the Atlantic."
Breaking German Enigma codes allowed the Allies to route convoys around U-boat patrol lines, cutting merchant ship losses by over two-thirds in July 1941. When Germany switched to a new four-rotor Enigma network called TRITON on the 1st of February 1942, Allied codebreakers went blind for ten months until Enigma material was salvaged from a foundering U-boat off Port Said on the 30th of October 1942.