How to do it...

Connect to the MySQL server:

shell> mysql -u root -p
Enter Password:
mysql> CREATE DATABASE company;
mysql> CREATE DATABASE `my.contacts`;

The back tick character (`) is used to quote identifiers, such as database and table names. You need to use it when the database name contains special characters, such as dot (.).

You can switch between databases:

mysql> USE company
mysql> USE `my.contacts`

Instead of switching, you can directly connect to the database you want by specifying it in the command line:

shell> mysql -u root -p company

To find which database you are connected to, use the following:

mysql> SELECT DATABASE();
+------------+
| DATABASE() |
+------------+
| company    |
+------------+
1 row in set (0.00 sec)

To find all the databases you have access to, use:

mysql> SHOW DATABASES;
+--------------------+
| Database           |
+--------------------+
| company            |
| my.contacts        |
| information_schema |
| mysql              |
| performance_schema |
| sys                |
+--------------------+
6 rows in set (0.00 sec)

The database is created as a directory inside data directory. The default data directory is /var/lib/mysql for repository-based installation and /usr/local/mysql/data/ for installation through binaries. To know your current data directory, you can execute:

mysql> SHOW VARIABLES LIKE 'datadir';
+---------------+------------------------+
| Variable_name | Value                  |
+---------------+------------------------+
| datadir       | /usr/local/mysql/data/ |
+---------------+------------------------+
1 row in set (0.00 sec)

Check the files inside data directory :

shell> sudo ls -lhtr /usr/local/mysql/data/ 
total 185M
-rw-r----- 1 mysql mysql   56 Jun  2 16:57 auto.cnf
-rw-r----- 1 mysql mysql  257 Jun  2 16:57 performance_sche_3.SDI
drwxr-x--- 2 mysql mysql 4.0K Jun  2 16:57 performance_schema
drwxr-x--- 2 mysql mysql 4.0K Jun  2 16:57 mysql
-rw-r----- 1 mysql mysql  242 Jun  2 16:57 sys_4.SDI
drwxr-x--- 2 mysql mysql 4.0K Jun  2 16:57 sys
-rw------- 1 mysql root  1.7K Jun  2 16:58 ca-key.pem
-rw-r--r-- 1 mysql root  1.1K Jun  2 16:58 ca.pem
-rw------- 1 mysql root  1.7K Jun  2 16:58 server-key.pem
-rw-r--r-- 1 mysql root  1.1K Jun  2 16:58 server-cert.pem
-rw------- 1 mysql root  1.7K Jun  2 16:58 client-key.pem
-rw-r--r-- 1 mysql root  1.1K Jun  2 16:58 client-cert.pem
-rw------- 1 mysql root  1.7K Jun  2 16:58 private_key.pem
-rw-r--r-- 1 mysql root   451 Jun  2 16:58 public_key.pem
-rw-r----- 1 mysql mysql 1.4K Jun  2 17:46 ib_buffer_pool
-rw-r----- 1 mysql mysql    5 Jun  2 17:46 server1.pid
-rw-r----- 1 mysql mysql  247 Jun  3 13:55 company_5.SDI
drwxr-x--- 2 mysql mysql 4.0K Jun  4 08:13 company
-rw-r----- 1 mysql mysql  12K Jun  4 18:58 server1.err
-rw-r----- 1 mysql mysql  249 Jun  5 16:17 employees_8.SDI
drwxr-x--- 2 mysql mysql 4.0K Jun  5 16:17 employees
-rw-r----- 1 mysql mysql  76M Jun  5 16:18 ibdata1
-rw-r----- 1 mysql mysql  48M Jun  5 16:18 ib_logfile1
-rw-r----- 1 mysql mysql  48M Jun  5 16:18 ib_logfile0
-rw-r----- 1 mysql mysql  12M Jun 10 10:29 ibtmp1