A fallacy is a logical error that invalidates the argument it is being used to make. All types of fallacy attempt to assert the truth of a statement on the basis of an illogical assumption. The most common types of fallacy include, but are not limited to, the appeal to authority, the argument from ignorance, fallacy of composition, and the correlation implies causation fallacy. While there are other types of fallacy, those other types are mostly derived from these or they are not as clearly associated with formal logical and rhetorical argument.
The appeal to authority is one of the most common of the types of fallacy. It basically involves an argument based on the assumption that if a person in authority believes an idea, it must be true on the merits of that person's authority alone. For example, if an expert in optical physics asserts that the sky is not blue but green, and he only uses his authority as an optical physicist to prove the point, he is using an appeal to authority. Obviously, not all appeals to authority are false, but the fallacy asserts that the actual reason for asserting the truth of a claim stems from the authority of the person expressing it, regardless of the actual truth of the matter.
In a similar way, the argument from ignorance muddles the connection between the truth of an argument and its fundamental nature. The argument from ignorance says that an assertion cannot be proven false, therefore it must be true. The argument from ignorance is most often employed for negative-outcome claims, such as "Aliens don't exist." Since it is impossible to prove that something doesn't exist, the argument from ignorance would insist that aliens do exist, citing the only proof the claim being that it cannot be proven false. The claim that aliens don't exist may be true, but the fact that it can't be proven isn't proof that it is false.
The fallacy of composition takes one factually true element to imply that the entire argument is true by association. In a similar way, the correlation implies causation fallacy uses a link between two true elements in an argument to suggest that one element directly causes the other. For example, an argument that asserts the link between good grades and good behavior is a causational one, with good grades creating good behavior. The data shows a link between the two elements but the fallacy arises from the possibility that good behavior may equally cause good grades.