In addition to the other two suggestions made, you might want to consider one of the books from the thread
Essential Books from Theravadin Resources. It was written with the exact need you have in mind: increasing understanding of dependent co-arising.
It's title is
The Great Discourse on Causation, The Mahanidana Sutta and Its Commentaries, and it was translated, compiled, and written by Bhikkhu Bodhi. It's been around for a while, and was the book I used to help me better understand this most important of concepts. It's only 140 pages long, but contains an in-depth analysis of dependent co-arising (or dependent arising, as some like to term it). I used to term it as "dependent origination," too, before I realized that "dependent arising" or, my preferred term, "dependent co-arising" was a more accurate term and way to characterize this phenomenon. This book comes well recommended (there may be others out there, but I have not recently searched for any that have addressed this study as I have been well served by the present book).
The blurb on the back of the book sums up it contents very well:
book blurb:
The Mahanidana Sutta, "The Great Discourse on Causation," is the longest and most detailed of the Buddha's discourses dealing with dependent arising (paticca samuppada), a doctrine generally regarded as the key to his entire teaching. The Buddha often described dependent arising as deep, subtle and difficult to see, the special domain of noble wisdom. So when his close disciple Ananda comes to him and suggests that this doctrine might not be as deep as it seems, the stage is set for a particularly profound and illuminating exposition of the Dhamma.
This book contains a translation of the Mahanidana Sutta together with all the doctrinally important passages from its authorized commentary and subcommentary. A long introductory essay discusses the rich philosophical implications of the sutta; an appendix explains the treatment of dependent arising according to the Abhidhamma system of conditional relations.