Fatal error: Call to undefined function imap_open() in PHP

Simple enough, the IMAP extension is not activated in your PHP installation. It is not enabled by default. If your local installation is running XAMPP on Windows, you have to enable it as described in the XAMPP FAQ:

Where is the IMAP support for PHP?

As default, the IMAP support for PHP is deactivated in XAMPP, because there were some mysterious initialization errors with some home versions like Windows 98. Who works with NT systems, can open the file "\xampp\php\php.ini" to active the php exstension by removing the beginning semicolon at the line ";extension=php_imap.dll". Should be: extension=php_imap.dll

Now restart Apache and IMAP should work. You can use the same steps for every extension, which is not enabled in the default configuration.

The Installation Procedure is always the same, but the package-manager and package-name varies, depending which distribution, version and/or repository one uses. In general, the steps are:

a) at first, user privilege escalation is required, either obtained with the commands su or sudo.

b) then one can install the absent PHP module with a package manager.

c) after that, restarting the apache2 HTTP daemon is required to load the module.

d) at last, one can run php -m | grep imap to see if the PHP module is now available.

On Ubuntu the APT package php5-imap (or php-imap) can bei installed with apt-get:

apt-get install php5-imap
service apache2 restart

On Debian, the APT package php5-imap can be installed aptitude (or apt-get):

aptitude install php5-imap
apache2ctl graceful

On CentOS and Fedora the RPM package php-imap can be installed with yum (hint: the name of the package might be something alike php56w-imap or php71w-imap, when using Webtatic repo):

yum install php-imap
service httpd restart

On systemd systems, while using systemd units, the command to restart unit httpd.service is:

systemctl restart httpd.service

The solution stated above has the problem, that when the module was already referenced in:

/etc/php5/apache2/php.ini

It might throw a:

PHP Warning:  Module 'imap' already loaded in Unknown on line 0

That happens, because it is referenced in the default php.ini file (at least on Ubuntu 12.04) and a PHP module must at most be referenced once. Using INI snippets to load modules is suggested, while the the directory /etc/php5/conf.d/ (that path may also vary) is being scanned for INI files:

/etc/php5/conf.d/imap.ini

Ubuntu also features proprietary commands to manage PHP modules, to be executed before restarting the web-server:

php5enmod imap
php5dismod imap

Once the IMAP module is loaded into the server, the PHP IMAP Functions should then become available; best practice may be, to check if a module is even loaded, before attempting to utilize it.