ERROR 1040 (HY000): Too many connections indicates that mysql has more than one connection
The first solution (not recommended) :
Need to wait for a period of time (quite long), let the existing connection timeout automatically released; Or restart mysql (CentOS7: SystemCTL Restart Mysqld.Service)
The second option (use with caution) :
Login to mysql: mysql-uroot-p your root password
Look at the maximum number of connections mysql is currently setting. In general, the default number of connections to mysql is over 100, and the maximum number can be set to 16384 (2 ^ 14)
show variables like ‘%max_connections%’;
Set the maximum number of connections as needed, so I’m going to set 1000 here
set GLOBAL max_connections = 1000;

Note: This is used with caution because once the server or mysql service is restarted, the Settings will not take effect and the default Settings will be restored
 
The third option (the conditions allow the recommended use) :
Add or modify the max_connections parameter in the mysql configuration file
Linux (centos7) environment:
Windows environment:
Find my.ini in the installation directory. If you don’t have it, find My-default.ini, make a copy and rename it my.ini. Add or modify the max_connections parameter
After setting parameters, restart mysql service.
 
Resources:
FAQ for Installing Mysql5.7 and mysql under Linux(Centos7)