First of all, ASP.NET is a request / response pipeline. This means that you are granted access to the request and response flows, as well as some provisions, such as session, cache, security, etc.
In addition, there are 3 frameworks for generating HTML. The first and oldest is known as ASP.NET Web Forms. Since it was the only one, it is sometimes called ASP.NET, but this does not correspond to the current state of things. ASP.NET MVC is the second, and there is a third, known as ASP.NET Web Pages. All three of them have the same main ASP.NET request / response pipeline and session, cache API ... What is the difference between the way they generate HTML.
You can check my answer to this question for more information. Asp.Net Web Forms and Asp.Net Web Pages
And to answer your specific question - no web forms go away. Many use it, MS releases new versions.
Web forms are pretty good for people with a desktop background because it uses a control model that is familiar to desktop developers and also has something that mimics state. It also requires less knowledge of HTML, JS, CSS. ASP.NET MVC is the opposite. This gives you a lot of control, but requires a lot of knowledge about the network.
I personally prefer web forms for MVC for a number of reasons, which I will not list here, but even supporters of Web Forms (and especially me) admit that web forms are a pretty bad way to learn about the network, as it abstracts a lot of things . This gives you performance, security, etc., but it can lead to cases of abstraction leakage if you donβt know how the underlying infrastructure works, and itβs pretty easy to skip learning the details, because you know things just work ... for now it will not break and then you do not know where to start.
Ultimately, the choice is yours, but if you start with web forms, be sure to learn about HTTP verbs, cookies, raw response flow, HTTP headers, html form / submit models Inline css vs individual files and javascript from the context of Web Forms and make sure that you know how Web Forms automates them.