The breaking of the German Enigma code (produced by a mechanical cipher) has often portrayed as a largely British affair but according to the authors (a Polish historian and a former Polish naval intelligence officer) it was the contributions of three Polish mathematicians in developing working models of the Enigma encoding machine that allowed the British to mount their codebreaking operation at Bletchley Park. This work describes the work of the Poles in the 1930s, their help in providing the codebreaking secrets to British and French Intelligence, and the contributions of the codebreakers to the Allied cause in World War II. Six appended essays examine peripheral topics such as the French contribution to the breaking of Enigma and the early days of the Polish Cipher Bureau.