I am still an undergraduate and I have taken courses like complex analysis and differential geometry. Also, I learnt myself manifold theory. (the book by Loring Tu).
Currently, I am quite interested in complex geometry, where I guess it is the intersection between complex analysis and geometry. But what is the roadmap for me to reach that research field? What particular mathematics is required? Do I need to learn PDE?
I'd suggest starting with something like smooth manifolds by John Lee together with some good text on elementary complex analysis, such as the classical book by Ahlfors. I'd then learn a little about sheaves from, e.g., Gunning and Rossi's classic book -- Analytic functions of several complex variables. Then I'd start working through Huybrechts' Complex Geometry, Principles of Algebraic Geometry by Griffiths--Harris, and for additional details Voisin's book on Hodge Theory and Complex Algebraic Geometry.