My local environment is:

• fresh Ubuntu 16.04
• with PHP 7

• with installed MySQL 5.7

  sudo apt-get install mysql-common mysql-server
  

When I tried to login to MySQL (via CLI):

mysql -u root -p

I came across an cyclic issue with 3 steps.

1) First was some socket issue

ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock'

Solution: restarting PC.

Which led to another error:

2) With access denied

ERROR 1698 (28000): Access denied for user 'root'@'localhost'.

Possible issue? Wrong password for "root" user!

Solution: reset root password with this tutorial.

With correct password and working socket, there comes last error.

3) Incorrect auth plugin

mysql "ERROR 1524 (HY000): Plugin 'unix_socket' is not loaded"

Here I stopped or somehow got to 1) again.

You can try as follows it works for me.

Start server:

sudo service mysql start

Now, Go to sock folder:

cd /var/run

Back up the sock:

sudo cp -rp ./mysqld ./mysqld.bak

Stop server:

sudo service mysql stop

Restore the sock:

sudo mv ./mysqld.bak ./mysqld

Start mysqld_safe:

 sudo mysqld_safe --skip-grant-tables --skip-networking &

Init mysql shell:

 mysql -u root

Change password:

Hence, First choose the database

mysql> use mysql;

Now enter below two queries:

mysql> update user set authentication_string=password('123456') where user='root';
mysql> update user set plugin="mysql_native_password" where User='root'; 

Now, everything will be ok.

mysql> flush privileges;
mysql> quit;

For checking:

mysql -u root -p

done!

N.B, After login please change the password again from phpmyadmin

Now check hostname/phpmyadmin

Username: root

Password: 123456

For more details please check How to reset forgotten password phpmyadmin in Ubuntu

The mysql command by default uses UNIX sockets to connect to MySQL.

If you're using MariaDB, you need to load the Unix Socket Authentication Plugin on the server side.

You can do it by editing the [mysqld] configuration like this:

[mysqld]
plugin-load-add = auth_socket.so

Depending on distribution, the config file is usually located at /etc/mysql/ or /usr/local/etc/mysql/

For Ubuntu 18.04 and mysql 5.7

• step 1: sudo mkdir /var/run/mysqld;

  step 2: sudo chown mysql /var/run/mysqld

  step 3: sudo mysqld_safe --skip-grant-tables & quit (use quit if its stuck )

login to mysql without password

• step 4: sudo mysql --user=root mysql

  step 5: SELECT user,authentication_string,plugin,host FROM mysql.user;

  step 6: ALTER USER 'root'@'localhost' IDENTIFIED WITH mysql_native_password BY 'root'

now login with

• mysql -u root -p <root>

You can try these some steps:

Stop Mysql Service 1st sudo /etc/init.d/mysql stop

Login as root without password sudo mysqld_safe --skip-grant-tables &

After login mysql terminal you should need execute commands more:

use mysql;

UPDATE mysql.user SET authentication_string=PASSWORD('solutionclub3@*^G'), plugin='mysql_native_password' WHERE User='root';

flush privileges;

sudo mysqladmin -u root -p -S /var/run/mysqld/mysqld.sock shutdown

After you restart your mysql server If you still facing error you must visit : Reset MySQL 5.7 root password Ubuntu 16.04

Try it: sudo mysql_secure_installation

Work's in Ubuntu 18.04

In case someone lands here after making the same mistake I did:

1. Switched to plugin="mysql_native_password" temporarily. Performed my tasks.
2. Attempted to switch back to the "auth_socket" plugin, but incorrectly referenced it as plugin="auth_socket" which resulted in mysql "ERROR 1524 (HY000): Plugin 'auth_socket' is not loaded"
3. Lacking a way to login to fix this mistake, I was forced to have to stop mysql and use mysql_safe to bypass authentication in order to switch to the appropriate plugin plugin="unix_socket"

Hopefully this saves someone some time if they receive the original poster's error message, but the true cause was flubbing the plugin name, not actually lacking the existence of the "auth_socket" plugin itself, which according to the MariaDB documentation:

In MariaDB 10.4.3 and later, the unix_socket authentication plugin is installed by default, and it is used by the 'root'@'localhost' user account by default.

I tried with and it works

use mysql; # use mysql table
update user set authentication_string="" where User='root'; 

flush privileges;
quit;

This may work

CREATE USER 'user'@'localhost' IDENTIFIED BY 'pwd';

ALTER USER 'root'@'localhost' IDENTIFIED BY 'MyNewPass';

You can try with the below commands:

hduser@master:~$ sudo /etc/init.d/mysql stop
[ ok ] Stopping mysql (via systemctl): mysql.service.
hduser@master:~$ sudo /etc/init.d/mysql start
[ ok ] Starting mysql (via systemctl): mysql.service.