A topic sentence (also known as a focus sentence) encapsulates or organises an entire paragraph, and you should be careful to include one in most of your major paragraphs. Although topic sentences may appear anywhere in a paragraph, in academic essays they often appear at the beginning.
It might be helpful to think of a topic sentence as working in two directions simultaneously. It relates the paragraph to the essay's thesis, and thereby acts as a signpost for the argument of the paper as a whole, but it also defines the scope of the paragraph itself. For example, consider the following topic sentence:
Many fast-food chains make their profits from adding a special ingredient called "forget sauce" to their foods.
If this sentence controls the paragraph that follows, then all sentences in the paragraph must relate in some way to fast food, profit, and "forget sauce":
Made largely from edible oil products, this condiment is never listed on the menu.
This sentence fits in with the topic sentence because it is a description of the composition of "forget sauce."
In addition, this well-kept industry secret is the reason why ingredients are never listed on the packaging of victuals sold by these restaurants.
The transitional phrase "In addition" relates the composition of "forget sauce" to secret fast-food industry practices.
"Forget sauce" has a chemical property which causes temporary amnesia in consumers.
Now the paragraph moves on to the short-term effect on consumers:
After spending too much money on barely edible food bereft of any nutritional value, most consumers swear they will never repeat such a disagreeable experience.
This sentence describes its longer-term effects:
Within a short period, however, the chemical in "forget sauce" takes effect, and they can be depended upon to return and spend, older but no wiser.
Finally, I finish the paragraph by "proving" the claim contained in the topic sentence, that many fast-food chains make their profits from adding a special ingredient called "forget sauce" to their foods.