TITLE: A Concrete Approach to Category Theory
QUESTION [11 upvotes]: Is there a way to learn Category Theory without learning so many concepts of which you have never seen examples?

REPLY [3 votes]: I must strongly disagree with most of the answers here. Lawvere/Schanuel introduces CT via (di)graphs instead of "algebraic" objects. This means it's basically on the Plato's-slave level of naive, visceral understanding, like set theory or high-school geometry. It also means it would be a wise read for even experienced mathematicians to really pump their intuitions about the subject. And, while it's indeed been used on actual high-school kids (the curious types who are often given set theory in your fancier schools), it will take you right up to adjunctions!
After that, Lawvere has written a more advanced book with Rosebrugh that is based on the category of sets, another worthwhile intuition pump even for the more advanced. But other than that, it's true that after Lawvere/Schanuel there's no real literature for you beyond that if you don't know algebra. Fortunately, you can take care of that quickly. Don't get scared by hard books like Lang or dry, matrix-heavy ones like Artin; pick up a Dover copy of Pinter (it's easy and fun!), learn a little linear algebra (yeah, you pretty much have to), be willing to keep learning a little more algebra from easy sources (e.g. internet stuff) even as you proceed with that CT you're so impatient to get to, and above all keep in mind the general idea of a structure, over and above a set, and what it would be for a morphism to preserve it. But yeah, you're ready for your first crack at Mac Lane! He's actually a really gentle writer, and the good thing about this subject is you can easily just use the examples you do understand for now, though of course the intuition comes easier the more you can relate to.
In sum: There is a way: Lawvere/Schanuel, one of the best books anyone will ever read. And I think it would be a tragedy if someone who's so excited and inspired by CT's abstract beauty were to be discouraged by all these dour warnings in an all-too-familiar "pay your dues kid; this stuff's a long and hard journey" spirit. Especially since algebra is so often made to seem so boring. (Really, it's not! And let CT be your motivation to uncover that particular pleasant surprise.)