Professor Balmer uses his own lecture notes. You start out with fundamentals of category theory, such as the Yoneda lemma and adjoint functors, and move on to group theory and ring theory. For group theory and ring theory, you will be covering similar material from Math 110AB, except for the facts that (1) you will use the language of category theory often so you'll wrap your head around familar concepts but in different language, and that (2) the pace of the course is three times faster. Professor Balmer's tests are hard - the average grade for the midterm was less than 50% and the average for final was around 60~70% - but he curves.
As category theory is covered in a very short amount of time, you may find the first two weeks of Math 210A, which is all about category theory, challenging. However, know that you will and can get through it, and that everyone else in your class is also struggling to learn category theory in such a short amount of time - so I would not be discouraged. I would definitely reach out to your peers to study together.
Whether or not it's Professor Balmer who is teaching Math 210A, I would not take this course if you don't have familiarity with all or most of what's covered in Math 110AB; you'll be crushed if you are taking this as your first abstract algebra course. Again, it's expected that you already know the Math 110AB material.
I would make sure that I am being courteous and respectful when I am engaging with Professor Balmer; he is very much approachable once you know that he appreciates courteousness. He is a very funny person, I laughed several times during his lectures. There is no attendance but his lectures go so fast. His lecture notes can be terse at times, so I would not hesitate to confer different books on abstract algebra as supplements if his lecture notes confuse you.
I would like to thank Professor Balmer for his teaching this course.