Learn Italian: Ho salutato il professore.

This is the passato prossimo (the recent past tense). To say "I greeted", you need two parts: the helper verb ho (I have) and the past participle of the verb salutare (to greet). For regular verbs ending in -are, you drop the -are and add -ato to get salutato. So, ho salutato literally translates to "I have greeted."

Why is there no word for "I" at the beginning of the sentence?

In Italian, subject pronouns like io (I) are usually left out. The helper verb ho already tells us exactly who is doing the action because it specifically means "I have". You would only say io ho salutato if you wanted to strongly emphasize that you did it, as opposed to someone else.

Does salutare only mean "to greet"?

Salutare is a very versatile verb! Here it means "to greet" or "to say hello to", but it is also used for "to say goodbye to". It comes from the same root as salute (health), because greeting someone traditionally meant wishing them good health.

Does il professore specifically mean a university professor?