This open access book presents theoretical framework and sample applications of variant construction. The first part includes the components variant logic, variant measurements, and variant maps, while the second part covers sample applications such as variation with functions, variant stream ciphers, quantum interference, classical/quantum random sequences, whole DNA sequences, and multiple-valued pulse sequences.Addressing topics ranging from logic and measuring foundation to typical applications and including various illustrated maps, it is a valuable guide for theoretical researchers in discrete mathematics; computing, quantum- and communication scientists; big data engineers; as well as graduate and upper undergraduate students.