If you're second year, then you're probably not that far off from having to taking a course in Abstract Algebra which spends a lot of its time developing the theory of groups and subsequently building off of it into other areas.

I quite like Pinter's book on Abstract Algebra and it only requires Velleman's How to Prove It. Pinter started with groups off the bat with a nice simple set of rules, and further elaborates its properties from the exercises. Although videos are quite helpful I had a hard time learning from them but they are a good motivator for learning the material, and I always believe nothing beats studying maths from a textbook.

I personally found the online lectures from Steven Roman to be good: https://youtube.com/playlist?list=PLiyVurqwtq0aHeXG4IEdtksIbhV-7pY2s

The accompanying book is not free though.

here are some lectures https://www.youtube.com/watch?v=VdLhQs_y_E8&list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5&index=1

and here is a website for a newer edition of the course https://people.math.harvard.edu/~bullery/math122/

both are harvards math122 class, but the first link is a collection of older recorded lectures, and the second link is a later course (unrecorded) on math122, but includes homework and some notes (so they shouldnt precisely be the same thing but should mostly overlap)

Check out the “visual group theory” lectures on YouTube. It opened my eyes after taking a standard group theory module

https://youtu.be/KufsL2VgELo?si=lC1w0DlXk9HUU8BQ

https://youtube.com/playlist?list=PLDcSwjT2BF_VuNbn8HiHZKKy59SgnIAeO&si=wf_RyhYKOboBAwrH

This video from 3blue1brown might be of interest to you: https://youtu.be/mH0oCDa74tE

I liked Fraleigh's group theory textbook. It doesn't go into great detail on all topics, but it hits the important stuff for a first pass. There used to be typed up solutions freely available online. You might check it out to see if they are still there.

Contemporary Abstract Algebra by Gallian

Fraleigh's abstract algebra book is good.

this series of videos!

I don't claim these are "the best resources," but I made some introductory group theory videos that I want you to know about: Abelian Groups Quiz, Hi, I'm the Klein Group, Sylow Theorem Practice Problem and there are a few more on my channel.

I love your whole channel! I'm watching your Linear Algebra series now.

What are you using? Which note take software? Are you using any sort of tablet?

I just sent the link to my brilliant nerdy tutor friend. She will love this.

Congrats! This is highly appreciated!

This is great! Thank you!

I hope you get big. Thank you!

Not a video, but visual group theory by Carter is a good read. Unfortunately I came across it too late for myself but I skimmed it and it gives some of the best explanations and justifications of any intro book I've seen.

Excellent lectures: https://www.youtube.com/watch?v=VdLhQs_y_E8&list=PLelIK3uylPMGzHBuR3hLMHrYfMqWWsmx5

Here's a set I started a few years ago:

https://www.youtube.com/playlist?list=PLKXdxQAT3tCs2Al22_PhYm0nXVE6hWm0E

I've learned a lot more about video production since then (and changed software), so maybe it's time to revisit these.

Try Artin’s Algebra book if you want it gentle and slow

I really enjoyed watching the Harvard lectures on Abstract Algebra (which covers Group Theory substantially) given by Benedict Gross. You can find the whole series here: http://matterhorn.dce.harvard.edu/engage/ui/index.html#/1999/01/82345

It's worth noting that you're probably looking for a first course in "representation theory (of groups)" rather than a course in basic group theory, though you may need some basic group theory to understand representation theory.

No regular course in group theory is going to study Young Tableau, and group representations will just be addressed as a side note at best.

Serre's Linear Representations of Finite Groups, Fulton-Harris Representation Theory are good texts for representation theory that will surely mention Young Tableaux.

It's worth noting that a lot of courses which are in "representation theory" focus on representation theory of Lie Algebras, which will surely be applicable but may not be what you're looking for.

For basic group theory, Dummit & Foote is the classic reference. Artin's Algebra is also respectable.

I doubt you're going to find a free online course in representation theory unless MIT opencourseware happens to have it or something. This sort of thing is usually delivered as a topics course to early graduate students or late undergraduate students of pure math. It may be worth seeing if a local math department has such a course and enrolling...

Others can give better advice probably, off the top of my head I know there are some group theory text books written specifically for physicists etc.

I'd like to recommend Frederic Schuller's course on the Geometric Anatomy of Theoretical Physics. The playlist is here on YouTube. It's a somewhat cursory, but very good series of subjects covering topology, Lie groups and algebras, and representation theory. He has another series aimed more towards General Relativity and another one that covers Quantum Mechanics. But the first one I mentioned will probably give you what you are looking for. I hope this helps!

The Brilliant course on group theory gets you from zero to actions and the Sylow theorems (a first course in finite group theory).

If you want to know about representation theory that should be a second course and there is no good similar resource that I know of (of course, there's plenty of books and notes). Fulton Harris starts with Young tableaux pretty early on I guess.

I'm no physicist but in the standard model aren't particles representations of Lie groups? I suspect you would benefit most from a course in Lie theory (Lie groups, Lie algebras and their representations), by-passing finite group theory and their representations. A mathematical physicist would know of a better reference, hopefully one of them reads your question.

I'm late to this post but if you are willing to leave out most of the topology Stillwell's Naive Lie theory is a good book and there is a lecture series I found that uses that book that I like here. It goes over matrix lie groups and is tailored for undergrads so its a lot more introductory. And also it mostly goes over U(n), SU(n), SO(n), and Sp(n) as well so it should help for what you want to learn about.

I'm a big fan of visual group theory on youtube: https://www.youtube.com/watch?v=UwTQdOop-nU

YES!
This was my introduction to group theory and I heavily recommend it.

Without any particular topic, this set of notes for example that I just found and skimmed are pretty good (there are many similar ones online, page 4 references the standard texts one should also at least skim), reading parts of Zee's book is also good to get started, these notes have way too much stuff but focusing on relevant stuff would be useful.

https://youtube.com/playlist?list=PLDfPUNusx1ErdQhrdAzincNJKgTQahsX_&si=QOq0WvIC9ru7ssqy

Georgi's book "Lie algebras in particle physics" is quite nice, especially the first chapters.

Just to add an additional reference, you can check out these lecture notes:

https://arxiv.org/abs/2109.12087

I also second the recommendation of the book by Georgi.

Schweigert and Fuchs. Thats all you will need.

Have you tried checking the website to see if they have these courses?