The lecture covers the grammatical structures of "wish" and "second conditional" to express desires. It discusses using "wish" with past tense verbs to talk about present wishes. It also covers the second conditional and its use of "if + past tense" in the if-clause and "would/could/might + bare infinitive" in the main clause to discuss hypothetical or unlikely situations. The lecture concludes with examples of using relative clauses, pronouns like "who/whom/that/which," and adverbs like "where/when/why" to provide additional information about nouns.