The Topics is Aristotle’s work on dialectical argument, and is generally less read than other works in the Organon (such as Categories and Posterior Analytics). The work is not about demonstration, but about arguments that take place in the course of a conversation. Instead of starting from certain first principles, arguments of this sort take their starting point from statements that are held by all, by the majority, or by the learned. Aristotle identifies four different areas where arguments can occur about a subject: its definition, its genus, its properties, its accidents.
Definition and genus both pertain to the essence of a thing, what it is. Property and accident are not part of the essence of a thing but belong to a thing: a property belongs to something essentially (it belongs to a man in virtue of his essence that is capable of laughter) whereas an accident does not. These are places (topika in Greek) around which arguments will take place.
The entire work is eight books long. The first book is introductory, looking at the sorts of premises that can be taken up in this work. He even acknowledges that it is possible to arrive at better definitions than he does, but that it is fine since the sorts of things he is talking about are approximate. The next six books then go through the sorts of rules that one should keep in mind when arguing about genus or definition or property or accident. A lot of these have to do with contraries. (It’s hard to think of examples off the top of my head.) To take a simple example, when considering whether something is correctly defined, look to see whether there is anything the definition should apply but does not, or anything that the definition does apply to but should not. When it comes to genus, how it is important to have the lowest possible genus, as this will also include all the higher genera, but not vice-versa. He clarifies that the rules he lays down are sometimes universally applicable, but sometimes only guides.
The final book deals with how to actually carry on arguments. He speaks of the sorts of propositions that should be conceded to an opponent, and which should not. He talks about how there are modes of dialectic that are aimed at arriving at the truth, but others in which one is simply trying to win a contest. In attempting to win a contest, it is better to try and have your opponent concede points that seem far removed from the matter at hand, since they are unlikely to admit something that is directly related to what is being proven. He speaks of “begging the question” as asking your opponent to admit a proposition that is identical or basically identical to the matter which is in dispute. Perhaps most importantly, he states that it is not wise to try to argue with just anyone on the street, or in a group of people, because in settings like this, people will often jump into using contentious arguments, and the whole discussion becomes fruitless.
If someone is going to engage in dialectic frequently, it is important to have arguments ready for the most common points of dispute, and also to have an arsenal of definitions for when it is likely that someone is going to use an ambiguous term. I was surprised that some of these tips for dialectic also appear at the beginning of the Cursus Philosophicus by John of St. Thomas. There he talks about how one says “I accept the minor” or “I deny the major” when arguing with someone; or one can say “I distinguish the major” when an ambiguous term is used, and then determine whether one accepts or rejects it according to which definition is meant.
Unlike the other works of the Organon, I think this one works fairly well as an audiobook. Though one could take out a notebook and diagram the sorts of rules and how they apply to each topic, it is practically more important to be able simply to recognize what is happening in an argument, and to uncover misleading steps.

—
For these posts, I will set a 10-minute timer and then write what I can for that time.
See also: A third round of classics