Reading package lists...Done
Building dependency tree
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mysql-server is already the newest version(5.7.21-0ubuntu0.16.04.1).
You might want to run 'apt-get -f install' to correct these:
The following packages have unmet dependencies:
mysql-server: depends: mysql-server-5.7 but it is not going to be installed
E: Unmet dependencies.Try 'apt-get -f install' with no packages(or specify a solution).
通过阅读错误信息可知，主要是因为依赖关系出现问题，主要思路是重建依赖关系，然后干净卸载，最后重装。
首先，更新系统
sudo apt-get update
然后，修复安装错误，会提示输入mysql用户名密码
sudo apt-get --fix-broken install
然后，检索mysql安装包，并删除检索出的依赖包，然后是删除/var/lib/mysql,最后重装mysql。
下面我把检索到的解决方法展示给大家：
We excute the following commands to solve the above problem:
1.Get the list of MySQL packages installed on the system by executing the command sudo dpkg -l grep mysql
2.Remove the packages shown above by executing the command
sudo apt-get --purge autoremove <packages from the step 1>
3. Delete /var/lib/mysql
4.Try to install mysql again.It should solve your problem.
第二步中的packages如下图所示：
最后就是更新系统并重装mysql
sudo apt-get update
sudo apt-get install mysql-server mysql-client
总结：
整体思路还是重建依赖关系，干净卸载，更新安装。希望对遇到相同问题不知所措的小伙伴有所启发、帮助。谢谢。