/usr/bin/sudo must be owned by uid 0 and have the setuid bit set

As you'll read on this answer on SO, this problem is not as hard as people are making it. You can get the sudo command working again without a reinstall by following these simple steps:

1. Log out as the current user, then log back in as root.
2. Execute chown root:root /usr/bin/sudo && chmod 4755 /usr/bin/sudo
3. Log out as root, then log back in as the current user.

This does the trick and is much quicker and less painful than the "nuclear option" recommended in other answers.

If your root password is not set, you can boot in Recovery Mode to set it.

Note that this will resolve the titular error /usr/bin/sudo must be owned by uid 0 and have the setuid bit set but if like the OP you did more than mess up the permissions of the /usr/bin/sudo file, a more "nuclear" option may in fact make more sense.

Back up your data and reinstall.

This probably looks extreme but this isn't just sudo. You destroyed the permission structure of your entire filesystem. Some of the other answers can get sudo working, but ignoring the whole problem is inviting a later disaster.

You could try to mirror the owners off another install but there are cases (/var/ for example) that are highly dependant on what you've actually got installed. If you want to get a scale of the problem, I've actually had a crack at helping somebody fix this sort of issue before. The fix is manual, long and could easily leave your system insecure or broken.

Picking through that mess is going to take considerably longer than a clean install.

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This has had a couple of drive-bys from folks that don't understand the seriousness of the situation here. To them it looks like a big pile of unnecessary work, the sort of thing a rogue plumber or mechanic says to shake you down for a bigger job.

If you've only changed the permissions on /usr/bin/sudo, by all means, just fix that. But this question is about a total system change. Every file (save the runtime-only ones) are now owned by the user. Everything the user runs (eg browsers, browser exploits) could then overwrite system files, spy on you, extract any data. This needs to be corrected. Per above, this is difficult. The easiest way is a reinstall.

So please, don't be lazy about this. Filesystem permissions help keep you safe, fix them.

1. go to recovery mode by keep pressing Esc while booting the system.

2. select root option in long list you can see after entering into recovery mode (it is actually root shell)

3. type command - mount -o remount / (Or in recovery you can click on grub option. This helped me get read-write permissions on the file system. This basically updated the read/write mode on the file system since the command wasn't working for me initially)

   It will remount your file system in read and write mode.

4. command - chown -R root:root /usr this command will change ownership from "user" to root again recursively

5. now still i had problem with sudo command, so I again followed step 1,2,3 and executed chmod 4755 /usr/bin/sudo

Now I really think that re-installing would have been really a "nuclear option"