Learn German: Bitte nicht gegen die Tür lehnen! - Please do not lean against the door!

This sentence uses an impersonal command, which is exactly what your current lesson covers! Using the infinitive at the very end of a phrase is a standard way to give general instructions, rules, or warnings to the public. You will see this structure everywhere on signs in Germany, like on train doors or in buses.

I learned that "to lean" (oneself) is the reflexive verb sich lehnen. Why is there no sich here?

You are perfectly correct! In standard spoken or written German, it would be sich gegen die Tür lehnen. However, in these shortened impersonal commands used on public signs, reflexive pronouns are often dropped to save space and make the warning as punchy and direct as possible.

Could I use an instead of gegen to say "against the door"?

Yes, you could say an die Tür, but there is a slight difference in nuance. An implies resting gently against a surface, whereas gegen suggests a more active force or weight pressing against a barrier. Signs on moving vehicles prefer gegen to emphasize that you shouldn't put your body weight against the doors. Also, remember that gegen always triggers the accusative case, giving us die Tür.

Why does nicht come before the prepositional phrase rather than at the end?