Thank you for your recommendation. Can you also recommend one about analytical number theory as it is the direction I would like to follow in my research.
For Partitions, I would suggest the book "An Introduction to Theory of Numbers" by G. H. Hardy and E. M. Wright as mentioned by Norbert Tihanyi but it would be better to start with the book "Number theory" by George E Andrews if you are a beginner to integer partitions.