A prominent issue in many contemporary philosophy of religion debates concerns whether the universe has a Designer. This book moves the discussion ahead in a significant way by devising an original deductive formulation of the Teleological Argument (TA) which demonstrates that the following are the only possible categories of hypotheses concerning fine-tuning and order: (i) chance, (ii) regularity, (iii) combinations of regularity and chance, (iv) uncaused, and (v) design. This book also demonstrates that there are essential features of each category such that, while the alternatives to design are unlikely, the Design Hypothesis is not, and that one can argue for design by exclusion without having to first assign a prior probability for design. By combining the TA with the Kalam Cosmological Argument (KCA) which it defends against various objections, this book responds to the God-of-the-gaps objection by demonstrating that the conclusion of the KCA-TA is not based on gaps which can be filled by further scientific progress, but follows from deduction and exclusion. This is an open access book.