Good question. Alone can be an adjective or an adverb whereas lonely is strictly an adjective. We use "alone" to describe several situations mainly, though, that there is one person by themselves without the presence of another. It's also used to show that a person will complete a task, travel to a particular place, or participate in something without the presence, help, or company of another person(s). Example: a. He's going to France alone for several months. b. I need to be alone today because I'm feeling tired and irritated. c. I'm going to study alone in the library for several hours tonight. As an adverb, we would see this used to show that something is restricted to particular subject. Example: a. The itinerary for the trip was created for her alone. *notice: this doesn't mean that she's going to travel alone rather the itinerary was made only with her in mind. She might be going alone but it doesn't automatically rule out that she might have company. b. This medical exam is being set up for him alone. *notice: the person receiving the exam may not be alone but the exam was designed specifically for him. Lonely describes a feeling, a state of mind due to circumstances and conditions of ones life. To be lonely would indicate that a person has no friends, no social life, and little fulfilling interaction with other people. It is also common that this feeling could be accompanied with feeling empty, sad, or depressed but it doesn't necessarily mean that it always does. Example: a. She feels lonely since her cat died because they were close for since she was a child. b. I'm starting to feel lonely because I haven't gone out much and most of my friends are busy or they moved away. c. He's a very lonely person, he has no friends and rarely goes anywhere outside of work.

thank you Alex !!!! thank you so much .. !

The word 'lonesome' has a similar meaning to 'lonely'. Or, actually, often the same exact meaning.

A person who is lonely is suffering because of social isolation. A person who is alone is just by him or her self.