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Voisin's book is quite (but not always) self-contained and well-written. For the supplementary references, you may use the first chapters of Griffiths-Harris "principles of algebraic geometry" which can help you to understand and motivate the complex backgrounds of complex Hodge theory. The book by Carlson, Müller-Stach, Peters, "Period mappings and Period domains" is more redable and self-contained than Voisin's book. The book by Bertin, Demailley, Illusie and Peters, "Introduction to Hodge theory" is less famous but a very good reference specially if you are interested in interactions between complex Hodge theory and Hodge theory in charac terstic $p$. Note that nowadays, there are a lot of online lecture notes that are simplified and can help you to understand the content of Voisin's book much more easily. Fro example this or this which is more detailed. By googling you can find even more references. Also, your background of representation theory can help you a lot a Hodge theory, as it constantly appears in studying Hodge theory and in Voisin's book (for example the very important notion of local systems is nothing but studying certain representations of the fundamental group).