There are many powerful methods used by the wrapper of jQuery. But i can't really discuss it right here as it will take too long to read. However, i will explain the api of each section of jQuery! This way it will make life easy for us when we are searching the api at jQuery official site!
jQuery Core contain all the functions available in jQuery that you need to extend, create, manipulate jQuery objects
It's like what the section name said! This section give you all the functions used by jQuery wrapper to filter its selection!
Attributes section provide you with all the functions available in jQuery to manipulate Attributes of DOM. This include CSS, attributes and properties.
This section provides all the functions jQuery have when chaining with jQuery.
jQuery text/DOM Manipulation functions.
jQuery CSS functions that manipulate the data in
All the special effects available in jQuery.
jQuery ajax functions that help reduce the risk of using Ajax technology and shorten the need to write lengthy codes for it.
This is the official documentation for jQuery UI, jQuery's visual controls. jQuery UI features a wide range of core interaction plugins as well as many UI widgets. The project homepage is located at jqueryui.com. Please visit these pages for downloading UI and many demos. (taken from the offical site)
Well, i believe once you guys have read the first basic tutorial of jQuery, this is basically just a lookup for people who want to know what each individual api is for. And seriously speaking, once you have done the first part of jQuery, working with jQuery isn't that difficult as long as you can read the api provided by jQuery team. For people who have foundation of such api from Java, this is a piece of cake!