Key ASP.NET 4.6 classes and their inheritance hierarchies

Below is a simplified at a glance view of key HTTP related classes.
This isn’t a complete list, so see the msdn.microsoft.com links if the type that you are looking is not found here.

This list may be updated in the future to include more types.

System.Web has been around since the beginning of ASP.NET and been growing and evolving for many years.
It includes System.Web.Http classes that are used by Web API

Full API reference at https://msdn.microsoft.com/en-us/library/gg145018.aspx

System.Web – classes and interfaces that enable browser-server communication
  Http – Contains classes of HTTP attributes.
   Controllers
   HttpActionContext – Information for the executing action.
   HttpActionContextExtensions – Extension methods for HttpActionContext
   HttpActionDescriptor – Information about the action methods
   HttpControllerContext – Information for a single HTTP operation
   HttpControllerDescriptor – Information that describes the HTTP controller
  HttpApplication – The base class for applications that are defined by the user in the Global.asax file
  HttpRequest – Read the HTTP values sent by a client during a Web request
  HttpResponse – Encapsulates HTTP-response information
  HttpRequestBase – The base class for classes that read HTTP request values. Abstract class that contains the same members as the HttpResponse class.
  HttpResponseBase – The base class for classes that provides HTTP-response information
  HttpResponseWrapper – Encapsulates the HTTP intrinsic object that provides HTTP-response information

System.Net is a relatively new assembly that is a core part of Web API

Full API reference at https://msdn.microsoft.com/en-us/library/gg145039(v=vs.110).aspx
System.Net – classes and interfaces that provide a simple programming interface for various network protocols including Http

  Http – A programming interface for modern HTTP applications

   Formatting – Classes for serializing and deserializing HTTP message body in a format based on the requested media type
   Handlers – Class of event handlers
   Headers – Classes related to HTTP headers