If you are concerned someone has been logging in to your Gmail to read your emails or send spam it is easy to check and see.
The first thing you need to do is open your web browser to https://security.google.com/
From here just click on recent events or – https://security.google.com/settings/security/activity
This gives you an idea geographically of where your account has been accessed from. If you see anything suspicious change your password or enable two step authentication! Two step authentication is a great feature in which you cannot access your Gmail without having your cell phone. Once you add it to your account if you ever try to login from an unknown place Gmail forces you to input a special code sent to you via text message.