Introduction to Temporal Mechanics and the Mathematics of Anti-Time presents a bold and accessible exploration of a new conceptual framework for understanding time and its deeper structure. In this thought-provoking article, Peter I. Kattan introduces the idea of anti-time-a weak, counter-directed temporal influence that complements ordinary forward time and enters system dynamics through future boundary conditions. Using clear explanations and minimal mathematics, the work shows how present evolution may be shaped not only by past causes but also by constraints associated with future states. Through illustrative examples drawn from physics, biology, psychology, and social systems, the article demonstrates how anti-time can be interpreted as a subtle "pull from the future" that stabilizes or biases present dynamics. The result is a compelling conceptual model in which time, under certain conditions, may transition from a flowing parameter into a structural dimension of reality. This is a short 26-page article on this topic.