If you don't want to install desktop downloader on your PC. Udemy offers a default download feature on their site- The Built-in Downloader Option. This solution is also helpful for you. The following are the website and steps:
https://www.udemy.com/
The Built-in Downloader of Udemy
Step 1. First you should log in the Udemy website, find the course categories on the top-left you want to learn.
Step 2. Hit Categories and choose a category you like. Next, scroll down to find the Filter option in a new page, then you can click the Filter button to spread the details. The following are all choices, including Topic, Price, Subcategory, Features, Level, Language, etc. You can choose the free courses from the Price tab.
Step 3. Enter the course, move your mouse on the gear to click it. If the instructor allows you to download, you can click it to download.
Step 4. Click the Download Lecture button to download Udemy course on your PC. Last you can click the Download icon on the top-right of the browser and hit the folder icon to watch downloaded course on your PC.
Please notice that the quality resolution of playing course in Udemy player must match the resolution that is downloaded.
Not only can you play Udemy videos on PC, but also on mobile phones. You need to download and install Android/iOS mobile app on your phone(https://www.udemy.com/mobile/). Here, I will take the iOS app as an example to show you how to download Udemy videos on iPhone. Operation on Android is similar.