There are two groups of researchers who are interested in designing network prools and who cannot (yet) effectively communicate with one another c- cerning these prools. The first is the group of prool verifiers, and the second is the group of prool implementors. The main reason for the lack of effective communication between these two groups is that these groups use languages with quite different semantics to specify network prools. On one hand, the prool verifiers use specification languages whose semantics are abstract, coarse-grained, and with large atom- ity. Clearly, prool specifications that are developed based on such semantics are easier to prove correct. On the other hand, the prool implementors use specification languages whose semantics are concrete, fine-grained, and with small atomicity. Prool specifications that are developed based on such - mantics are easier to implement using system programming languages such as C, C++, and Java. To help in closing this communication gap between the group of prool verifiers and the group of prool implementors, we present in this monograph a prool specification language called the Timed Abstract Prool (or TAP, for short) notation. This notation is greatly influenced by the Abstract Prool Notation in the textbook Elements of Network Prool Design, written by the second author, Mohamed G. Gouda. The TAP notation has two types of sem- tics: an abstract semantics that appeals to the prool verifiers and a concrete semantics thatappeals to the prool implementors group.