Can I use youtube videos on my own website without having a copyright infringement?

If the creators of the videos allow embedding, you can embed the videos in your Web site, using the embedding code provided by YouTube with the embedded player. The creators of videos explicitly allow this as part of the YouTube terms of service, so it's not copyright infringement. YouTube does place some restrictions on whether or not you can put advertising on the same page as the videos, however (you need to have other content on the page besides the video if you plan to use advertising).