Base class of .net?

System.Object is the base class of .NET.

                                  It Supports all classes in the .NET Framework class hierarchy and provides low-level services to derived classes. This is the ultimate superclass of all classes in the .NET Framework; it is the root of the type hierarchy.

                                                     Base class is a root class or superior class from which we can extend classes.it is the topmost in the classes so other classes can be derived from this class but it is not derived from any class.Depending on procedure base class may or may not give its objects to derived classes of it. 
system.Web.UI is for asp.net

The super most base class is system.object. even the system.web.ui comes from the system.object. All the object of type either value or reference type come from system.object. see the msdn doc for the same.