Why my SSD keeps getting full of logs?

Question

I have an Ubuntu Gnome installation on my 128GB SSD, with the /home mounted on another harddisk. I keep getting alerts that my disk is full. When I open the Disk Usage utility, I see this:

When I try ls -la in the terminal, I get this result:

ls -la
total 87744216
drwxrwxr-x 12 root    syslog         4096 Nov  2 08:20 .
drwxr-xr-x 15 root    root           4096 Oct 16 18:59 ..
-rw-r--r--  1 root    root              0 Nov  1 08:39 alternatives.log
-rw-r--r--  1 root    root          49237 Oct 26 17:28 alternatives.log.1
drwxr-x---  2 root    adm            4096 Nov  2 08:04 apache2
-rw-r-----  1 root    adm               0 Nov  2 08:04 apport.log
-rw-r-----  1 root    adm          103025 Nov  2 08:04 apport.log.1
-rw-r-----  1 root    adm             117 Oct 30 19:04 apport.log.2.gz
-rw-r-----  1 root    adm             945 Oct 27 08:54 apport.log.3.gz
-rw-r-----  1 root    adm             249 Oct 21 21:53 apport.log.4.gz
-rw-r-----  1 root    adm             447 Oct 21 09:22 apport.log.5.gz
-rw-r-----  1 root    adm             237 Oct 17 15:27 apport.log.6.gz
-rw-r-----  1 root    adm             373 Oct 17 11:20 apport.log.7.gz
drwxr-xr-x  2 root    root           4096 Nov  1 13:52 apt
-rw-r-----  1 syslog  adm          118832 Nov  2 08:24 auth.log
-rw-r-----  1 syslog  adm          139959 Oct 29 08:01 auth.log.1
-rw-r-----  1 syslog  adm            9736 Oct 22 09:00 auth.log.2.gz
-rw-r--r--  1 root    root           5990 Nov  2 08:20 boot.log
-rw-r--r--  1 root    root          59400 Apr 12  2017 bootstrap.log
-rw-------  1 root    utmp              0 Nov  1 08:42 btmp
-rw-------  1 root    utmp              0 Apr 12  2017 btmp.1
drwxr-xr-x  2 root    root           4096 Nov  2 08:04 cups
drwxr-xr-x  2 root    root           4096 Apr 11  2017 dist-upgrade
-rw-r--r--  1 root    root           1801 Nov  1 13:52 dpkg.log
-rw-r--r--  1 root    root        1751113 Oct 31 22:56 dpkg.log.1
-rw-r--r--  1 root    root          32032 Oct 28 10:52 faillog
-rw-r--r--  1 root    root           4208 Oct 26 18:54 fontconfig.log
drwx--x--x  2 root    gdm            4096 Oct 27 08:54 gdm3
-rw-r--r--  1 root    root           2303 Nov  2 08:20 gpu-manager.log
drwxr-xr-x  3 root    root           4096 Apr 12  2017 hp
drwxrwxr-x  2 root    root           4096 Oct 16 18:54 installer
-rw-r-----  1 syslog  adm     44844350535 Nov  2 08:26 kern.log
-rw-r-----  1 syslog  adm     32755816806 Oct 29 08:04 kern.log.1
-rw-rw-r--  1 root    utmp         292292 Oct 28 10:52 lastlog
-rw-r-----  1 syslog  adm            1419 Nov  2 08:20 mail.log
-rw-r-----  1 syslog  adm            2087 Oct 29 07:57 mail.log.1
drwxr-xr-x  2 mongodb mongodb        4096 Oct 29 08:02 mongodb
-rw-r-----  1 syslog  adm       155708327 Nov  2 08:26 syslog
-rw-r-----  1 syslog  adm      9303776069 Nov  2 08:05 syslog.1
-rw-r-----  1 syslog  adm       304397086 Nov  1 08:42 syslog.2.gz
-rw-r-----  1 syslog  adm       541693693 Oct 31 07:03 syslog.3.gz
-rw-r-----  1 syslog  adm       602717000 Oct 30 09:17 syslog.4.gz
-rw-r-----  1 syslog  adm       695496075 Oct 29 08:04 syslog.5.gz
-rw-r-----  1 syslog  adm       639882787 Oct 28 09:03 syslog.6.gz
-rw-r-----  1 syslog  adm         3567386 Oct 27 08:59 syslog.7.gz
drwxr-xr-x  2 root    root           4096 Oct 27 11:57 teamviewer12
drwxr-x---  2 root    adm            4096 Nov  1 08:42 unattended-upgrades
-rw-rw-r--  1 root    utmp           5376 Nov  2 08:20 wtmp
-rw-rw-r--  1 root    utmp          60672 Nov  1 08:35 wtmp.1

It seems like the kernel logs are huge.

Did anyone run into this problem? What could be it and how can it be solved?