Here are some books I recommend on gender identity and related issues such as homosexuality and transgenderism.
Top Recommendation

The Rise and Triumph of the Modern Self
While The Rise and Triumph of the Modern Self is a demanding read, especially for those of us for whom many of these categories and characters are unfamiliar, it is a rewarding read. In its pages Trueman aptly explains how and why our culture has arrived at a place where “I am a woman trapped in a man’s body” is no longer nonsensical, no longer self-contradictory. And it begins to explain what is at stake if this long march is not interrupted, not refuted according to truth. (See also the briefer Strange New World.)
Other Recommendations

Does God Care About Gender Identity?
This is a brief but helpful book that describes the issue and suggests how to respond to it.

This was written to provide a biblical, biological, and compassionate response to the modern day gender ideology that has been flooding our world and sweeping away so many victims.

Branch’s book is meant to inform Christians about the growing transgender debate and to show Christians how the Bible speaks to the issue.

shows that the modern issues of identity are really just the age-old issue of pride.

Shrier is not a Christian but writes about the issue of transgenderism and especially how it is impacting young girls.

This book will help Christians better understand and better respond to one of the most pressing issues of our time. And even better, it will help them show compassion and bring healing to those who have been swept up in it.

One woman’s journey through gender confusion, reassignment surgery, and detransitioning. Her story is sad and tragic, yet also powerful and encouraging.

Hough answers the practical questions with wisdom and grace. He speaks the truth in love—true love that will not affirm what God forbids.

A Field Guide on Gender and Sexuality
A helpful, timely, and valuable resource that offers sound answers to urgent questions. It is priced very reasonably, which makes it ideal to purchase in bulk and distribute widely.
(See also my recommendations on parenting for books that help parents address these issues with their children.)