Integrate Google calendar

Google has an extensive API available. Depending on your use case, which you did not mention, I would start with that.

I need to display all the events on my google calendar to be displayed in Appian

You can follow the link below for API reference documentation to list all google calendar events of the given user.
https://developers.google.com/calendar/api/v3/reference/events/list

You can create a connected system in Appian to store base URL and authentication information and use the Integration Object to hit the API.

In order to get connected with google APIs you need to create a project at https://console.cloud.google.com/welcome

There you choose the authentication mode you and get the credentials to be used in the connected system in Appian.

First we will be giving the event details in appian. Those event details should be reflected in google calendar. For event timings user need to be notified with an email.

First we will be giving the event details in appian. Those event details should be reflected in google calendar. For event timings user need to be notified with an email.