How to use jquery library in Magento 2?

If you are adding your custom js library other than jQuery then you need to include the js code inside require function like:

 require(['jquery', 'jquery/ui'], function($){ 
     //your js code here  
 });

Examples:

Inside the require function, you can directly access jQuery functionality in place by using either jQuery or its short form alias, the dollar $ sign. For example:

require(['jquery', 'jquery/ui'], function($){
  jQuery(document).ready( function() {
    alert("Page loaded.");
  });
});

Here is an example with the $ alias:

require(['jquery', 'jquery/ui'], function($){
  $(document).ready( function() {
    alert("Page loaded.");
  });
});

Jquery/JqueryUI have added in magento2. You can see in lib/web/jquery

To use jquery or call widget of magento. From your js file

define([
  'jquery',
  'jquery/ui',
  'mage/<widget.name>' found in /lib/web/mage dir
], function($){

$.widget('<your_namespace>.<your_widget_name>', $.mage.<widget.name>, {  CODE HERE... });

return $.<your_namespace>.<your_widget_name>;

});