I don’t really understand what you mean by “from first principles” here. Do you mean in a way that’s intuitive to you? Or in a way that includes all the proofs?
Any field of Math is typically more general than any one intuition allows, so it’s a little dangerous to think in terms of what it’s “really” doing. I find the way most people learn best is by starting with a small number of concrete intuitions – e.g., groups of symmetries for group theory, or posets for category theory – and gradually expanding.
In the case of Complex Analysis, I find the intuition of the Riemann Sphere to be particularly useful, though I don’t have a good book recommendation.
I don’t really understand what you mean by “from first principles” here. Do you mean in a way that’s intuitive to you? Or in a way that includes all the proofs?
Any field of Math is typically more general than any one intuition allows, so it’s a little dangerous to think in terms of what it’s “really” doing. I find the way most people learn best is by starting with a small number of concrete intuitions – e.g., groups of symmetries for group theory, or posets for category theory – and gradually expanding.
In the case of Complex Analysis, I find the intuition of the Riemann Sphere to be particularly useful, though I don’t have a good book recommendation.