JS Bin// source https://jsbin.com/xifegud

jsbin.xifegud.js

let courses = [  
   {  
      "title":"ttile 1",
      "id":"1",
      "course_cat":"introduction"
   },
   {  
      "title":"title 2",
      "id":"2",
      "course_cat":null
   },
   {  
      "title":"blabla 1",
      "id":"3",
      "course_cat":"test"
   },
   {  
      "title":"blabla 2",
      "id":"4",
      "course_cat":null
   }
];

let grouped = courses.reduce((allCourses, course) => {
  allCourses[course.course_cat] = [...allCourses[course.course_cat] || [], course];
  return allCourses;
}, {});

console.log(grouped);