Basic formal systems

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I'm studying history but I always loved math. So my question is, what math topic is simple to learn, but still fullfills my need to think mathematically? I have some experience in basic group-theory and some physics, mostly self taught. My own idea is to learn about formal mathematical systems, but the ones I found are either too complex or too simple. Or maybe combinatorics or geometric algebra are enought. Not sure. It should be a simple but deep topic that is easy to learn and be mostly self contained.