Calculus on time scales was established in 1988 by Stefan Hilger. It includes both the classical derivative and the forward difference operator as special cases. It also includes Riemann integrals and finite sums as inverse operations. However, it does not include the Jackson q-difference operator on the real numbers and the Jackson q-integral on R. Also, it does not include neither the difference operator on R and associated Norlund sums nor the Hahn difference operator. This book extends the definition of time scales in a way such that the previous difference operators and their associated sums are included. In addition, new illustrative examples will be given.