Install dovecot with apt-get install dovecot-imapd
Dovecot version and config file
# 2.2.9: /etc/dovecot/dovecot.conf
Linux Server (it will work with new versions with little or no adjustment)
# OS: Linux 3.13.0-116-generic x86_64 Ubuntu 14.04.5 LTS
Edit your /etc/dovecot/dovecot.conf file. See file dovecot.conf.
You have to create the file /etc/dovecot/users as below:
To generate the password, execute doveadm
doveadm pw -s SHA512-CRYPT (the password will be prompted)
The command returns something like this, put this string inside /etc/dovecot/users and save.
user:{SHA512-CRYPT}$6$2TEJo6hStd3.NgQs$5nIeyUn/1bA4.dptvfsQ0wtU1XtnSqGRSkmn5bV5OcJRRAurmYxdaUcgOpEpQSLbHmKwhgRa9ik18TN6ckVuH0:1000:1000::/home/user
I will not cover SMTP here, but you can install Exim4 or postfix (MTA) and combine the use with Dovecot (MDA) if you like, there are many options out there.
That's All! Enjoy your new mail server.