When I type the command "last reboot" I get the following output:

user@computer:~$ last reboot
reboot system boot 4.4.0-53-generic Wed Dec 14 07:50 - 09:36 (01:46)
reboot system boot 4.4.0-53-generic Wed Dec 14 06:53 - 09:36 (02:43)
reboot system boot 4.4.0-53-generic Wed Dec 14 03:51 - 09:36 (05:45)
reboot system boot 4.4.0-53-generic Wed Dec 14 02:11 - 09:36 (07:25)
reboot system boot 4.4.0-53-generic Wed Dec 14 00:07 - 09:36 (09:29)
reboot system boot 4.4.0-53-generic Tue Dec 13 20:47 - 09:36 (12:48)
reboot system boot 4.4.0-53-generic Tue Dec 13 19:50 - 09:36 (13:46)
reboot system boot 4.4.0-53-generic Tue Dec 13 17:17 - 09:36 (16:18)

What I know for certain is that I did a manual reboot at 17:17 yesterday and logged in this morning at 09:36. What are all the entires in between those times? Does it mean my computer is rebooting again and again overnight when no-one is using it?

That seems to be contradicted by the last column, which looks like the duration of the session. The session started at 17:17 lasted 16:18 hours (and counting).

Thanks for any info! x

I take it you gave this command at 9:36 immediately after logging in. I agree the output is weird. The next place to look is your system logs, especially /var/log/messages. If you have systemd, you might find useful information through journalctl as well.

Install Snoopy, set it up, it logs everything.

which reminds me I need to do that again, I just did a re-install of my system.

oo