A topic sentence or point sentence — usually the opening statement of a paragraph — is an assertive statement indicating both the paragraph’s topic and your position on this topic. It usually contains or follows some sort of transition from the topic of the previous paragraph (see “trans”).
Topic sentences are important signals to your reader about the direction of your argument; if they are good, they will also help you define and organize your argument.
Avoid beginning a paragraph with a simple statement of fact or a narrative summary. “Hermione first begins her speech by talking to her husband, Leontes, about getting Polixenes to stay in Sicilia” is not an argumentative statement. No one would dispute the denotation of Hermione’s appeal at 1.2.28 of The Winter’s Tale. Trust your reader to know what the play is about.
Make sure that the topic sentence does justice to the contents of your paragraph.
Likewise, make sure that the entire paragraph addresses the issue identified in the topic sentence as the subject of the paragraph.
See “Using Topic Sentences” (webpage at the University of Toronto).