Publicly accessible (outlook) calendar ASP.NET

My goal is to create a web app (ASP.NET MVC) which has a (outlook) calendar, that can be accessed publicly. So every person can create an appointment.

It is also necessary that the created appointments sync with the calender of an outlook account.

Where should I start looking? I have experience with ASP.NET MVC developing, so I'm searching solely how to get the calender functionality.