Mac just restarts but does not update

You don't have enough free space. During installation, you should have at least 20GBs of free space. Most of it will be returned after installation.

Please read Writing an effective Apple Support Communities question. We are here to help. We are all users. We are not mind-readers nor clairvoyants. We only know what you write down and tell us. Be specific and thorough. Try to write clearly. Think about what you want to say before you write it down, then re-read it to see if it makes sense. We need the following at a minimum:

• What specific product model do you have? Avoid just saying, "iPhone or Mac," because that doesn't describe it uniquely.
• Tell us the version of iOS or Mac OS that you have installed on your machine.
• Provide a short but complete summary of your question, problem, or issue. (No complaints, please.)
• Give us all the details of your question, problem, or issue. Make your descriptions clear and precise but don't be wordy. Like Joe Friday used to say, "Just the facts." Be sure you provide any other details that we should know.
• Detail what you have tried, so far, to solve your problem even if it's "nothing."
• Provide images/snapshots appropriate to your descriptions. Pictures are worth 1,000 words.

Note: If English is not your native language, please let us know. Perhaps you would be better served by posting in your native language. If you do, then understand that getting a reply may take more time. Most of the helpers are native English speakers but some of us are bi- or multi-lingual. Unfortunately, English is my only language. I am able to use translators if I know what your native language is. However, I will be slower in responding.

FYI: These are user-only communities. This is not Apple Support. if you need to contact Apple Support, then contact product and tech support: Contacting Apple for support and service includes international calling numbers.

The Apple Support Communities only provides help for users of Apple products. Apple does not read theae forums. If you wish to provide feedback to Apple, then go to Apple Feedback. Thank you for your understanding and support.