CREATE {DATABASE | SCHEMA} [IF NOT EXISTS] db_name
    [create_option] ...
create_option: [DEFAULT] {
    CHARACTER SET [=] charset_name
  | COLLATE [=] collation_name
}
      CREATE DATABASE creates a database
      with the given name. To use this statement, you need the
      CREATE privilege for the database.
      CREATE
      SCHEMA is a synonym for CREATE
      DATABASE.
    
      An error occurs if the database exists and you did not specify
      IF NOT EXISTS.
    
      CREATE DATABASE is not permitted
      within a session that has an active LOCK
      TABLES statement.
    
      Each create_option specifies a database
      characteristic. Database characteristics are stored in the
      db.opt file in the database directory. The
      CHARACTER SET option specifies the default
      database character set. The COLLATE option
      specifies the default database collation. For information about
      character set and collation names, see Chapter 10, Character Sets, Collations, Unicode.
    
      To see the available character sets and collations, use the
      SHOW CHARACTER SET and
      SHOW COLLATION statements,
      respectively. See Section 13.7.5.3, “SHOW CHARACTER SET Statement”, and
      Section 13.7.5.4, “SHOW COLLATION Statement”.
    
      A database in MySQL is implemented as a directory containing files
      that correspond to tables in the database. Because there are no
      tables in a database when it is initially created, the
      CREATE DATABASE statement creates
      only a directory under the MySQL data directory and the
      db.opt file. Rules for permissible database
      names are given in Section 9.2, “Schema Object Names”. If a database
      name contains special characters, the name for the database
      directory contains encoded versions of those characters as
      described in Section 9.2.4, “Mapping of Identifiers to File Names”.
    
      If you manually create a directory under the data directory (for
      example, with mkdir), the server considers it a
      database directory and it shows up in the output of
      SHOW DATABASES.
    
When you create a database, let the server manage the directory and the files in it. Manipulating database directories and files directly can cause inconsistencies and unexpected results.
MySQL has no limit on the number of databases. The underlying file system may have a limit on the number of directories.
You can also use the mysqladmin program to create databases. See Section 4.5.2, “mysqladmin — A MySQL Server Administration Program”.