 On the one hand, the argument arises from human curiosity as to why there is something rather than nothing or than something else. It invokes a concern for some full, complete, ultimate, or best explanation of what exists contingently. On the other hand, it raises intrinsically important philosophical questions about contingency and necessity, causation and explanation, part/whole relationships (mereology), possible worlds, infinity, sets, the nature of time, and the nature and origin of the universe. In what follows we will first sketch out a very brief history of the argument, note the two basic types of deductive cosmological arguments, and then provide a careful analysis of examples of each: first, three arguments from contingency, one based on a relatively strong version of the principle of sufficient reason and two others based respectively on a very strong and on a weak version of that principle; and second, an argument from the alleged fact that the universe had a beginning and the impossibility of an infinite temporal regress of causes. In the end we will consider an inductive version of the cosmological argument and what it is to be a necessary being.