This book introduces the recent progress on the multiplier conjecture, prime power conjecture, Lander conjecture; including the author's and his graduate student T Feng's work on the multiplier conjecture. It provides a sufficiently broad introduction to algebraic approach for studying difference sets, including group ring, representation theory of finite groups, cyclotomic fields, etc. It also introduces the intricate relationships between difference sets and cryptography, for example, quasi-perfect sequences and cyclic (4n–1, 2n–1, n–1)- difference sets, bent functions and Hadamard difference sets, perfect nonlinear maps and semiregular relative difference sets.