wget http://repo.zabbix.com/zabbix/3.2/ubuntu/pool/main/z/zabbix-release/zabbix-release_3.2-1+xenial_all.deb
dpkg -i zabbix-release_3.2-1+xenial_all.deb
apt-get update
apt-get install zabbix-server-mysql zabbix-frontend-php

Creating initial database

Create Zabbix database and user on MySQL by the following commands, where <root_password> shall be replaced with the actual root password (e.g., shell> mysql -uroot -p12345) and <password> with new password for zabbix user on the database (including apostrophes: …identified by '67890';):

shell> mysql -uroot -p<root_password>
mysql> create database zabbix character set utf8 collate utf8_bin;
mysql> grant all privileges on zabbix.* to zabbix@localhost identified by '<password>';
mysql> quit;

$sudo service mysql stop
$sudo mysqld_safe --skip-grant-tables

# Another terminal
$mysql -uroot mysql
mysql > update user set password=PASSWORD("root") where User='root';
mysql > flush privileges;
mysql > quit;
$ sudo service mysql restart
$ mysql -uroot -proot
ERROR 1698 (28000): Access denied for user 'root'@'localhost'

dpkg -l | grep mysql
ii  libdbd-mysql-perl                     4.033-1ubuntu0.1                                            amd64        Perl5 database interface to the MySQL database
ii  libmysqlclient20:amd64                5.7.17-0ubuntu0.16.04.1                                     amd64        MySQL database client library
ii  mysql-common                          5.7.17-0ubuntu0.16.04.1                                     all          MySQL database common files, e.g. /etc/mysql/my.cnf
ii  php-mysql                             1:7.0+35ubuntu6                                             all          MySQL module for PHP [default]
ii  php7.0-mysql                          7.0.13-0ubuntu0.16.04.1                                     amd64        MySQL module for PHP
ii  zabbix-server-mysql                   1:3.2.3-1+xenial                                            amd64        Zabbix network monitoring solution - server (MySQL)

mysql_secure_installation