Computation Complexity books for a mathematician

I recently attented to some computational complexity (or complexity theory, I am not sure which is the correct name) and I fell in love with it. I would like to find some books, online courses… in general resources of any kind to self-study this (securely) wonderfull subject.

My backgrund is pure mathematics with emphasys in discrete mathematics (graph theorey, crypto, coding thoery, combinatorics…), with no background in computer science. I am not sure if the last one is mandatory.