Introduction to Cosmology
Here are some resources to help learn cosmology. They are all free!
I have tried to arrange the entries in each section in an order of ease of understanding. The entries start easy and get harder (ie more maths and physics) the lower down the section order.
There are many resources on the Internet and the lists below are just a few I found particularly helpful.
Don’t be afraid about the “big topics” of physics like General Relativity (GR). A full understanding is not required. The EdX course gradually introduces GR topics that are needed to study cosmology.
Certainly do not be afraid to get stuck into arXiv! Yes, there are very technical papers there with subjects that are seemingly incompressible. This is fine and entirely normal  and remember, even professional physicists don’t know everything and have to research things!
It’s part of the fun and joy of learning.
Above all, have fun and enjoy!
Sites & Courses

Ned Wright’s Introduction to Cosmology
The FAQ section is superb!
There are also nice explanations about the CMB. 
This is a more detailed study from libretexts and involves more mathematics.

Cosmology Course, self paced from edX
This is an excellent free course (even though it pushes for a certificate that is not free  this is optional). I thoroughly recommend the course. It has recently been updated to include fresh developments.
Would also suggest the Greatest Unsolved Mysteries of the Universe first if you are unfamiliar with basic cosmology terminology.
Videos

Standford Cosmology Course with Leonard Susskind (part of the Theoretical Minimum)
Leonard Susskind teaches a cosmology course as part of the Theoretical Minimum series. He covers the absolute bare minimum required to understand the topic.
The strapline is “For those in a hurry …”, and the course is for mature students. So its a good solid course but without the rigour and hence subtleties of the subject, but a good introduction/grounding nevertheless. There are other areas of physics, see resources below.

World Science U Masterclass  Alan Guth  Inflationary Cosmology

MIT OpenCourseWare, Alan Guth  Inflationary Cosmology
Similar to the World Science U masterclass but more detailed and technical!
Resources

This site is in the process of being updated, however there is a course on Special Relativity run by Brian Greene. It’s a university level, fully mathematical course, with lots of visuals and problem sets. Really excellent stuff and entirely free!

arXiv  TASI Lectures: Introduction to Cosmology, Trodden M, Carrol SM

arXiv  The Physics of Microwave Background Anisotropies, Hu, Sugiyama, & Silk
Tags
#cosmology