John Piper's work on eldership, salvation, and practical theology have shaped my beliefs as much as any other modern pastor. He is a Biblical thinker and one of the most important Christian authors in the modern era. The sheer amount of pages he has produced in his career is staggering.
Finally Alive is one of his newest, and it is a great read for new Christians. Why should we be born again? How are we born again? What is the Holy Spirit's role in salvation? These, and many more questions regarding the new birth, are answered in this short book. I thought the best part of the book was the last section on sharing the gospel, How Can We Help Others Be Born Again? His Ten Encouragements for Gospel-Telling near the end of this section are very practical and were the highlight of Finally Alive.
Piper's numerous works understandably have a lot of overlap, but I think Finally Alive is one that contains enough new material to make it worth your while, even if you have read much of what he has put out already. This book is geared towards those who would like to know more about being "born again." When people ask me which Piper books I recommend reading, I always recommend The Dangerous Duty of Delight first (this is the basically the cliff notes for Desiring God), and Don't Waste Your Life next. These books are short, readable, and life-changing. While Finally Alive may not be my first recommendation, it is certainly on the short list and would be a great one to pick up.