It was a brazen bank heist, but a 21st-century version in which the criminals never wore ski masks, threatened a teller or set foot in a vault. In two precision operations that involved people in more than two dozen countries acting in close coordination and with surgical precision, thieves stole $45 million from thousands of A.T.M.'s in a matter of hours. In New York City alone, the thieves responsible for A.T.M. withdrawals struck 2,904 machines over 10 hours starting on Feb. 19, withdrawing $2.4 million. The operation included sophisticated computer experts operating in the shadowy world of Internet hacking, manipulating...